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IMA Newsletter #348

October 2005

2005-2006 Program


See http://www.ima.umn.edu/2005-2006 for a full description of the 2005-2006 program on Imaging.

News and Notes

Fall IMA Seminars

As part of the 2005–2006 thematic program Imaging, the following seminar series will be offered this fall:

In addition, there will be an informal seminar series on Applications of approximation theory to imaging compression, organized by Brad Lucier and Steve Damelin, meeting most Wednesdays 11:15–12:15 in 409 Lind Hall, and an informal seminar/working group on Object recognition, organized by Peter Olver, with meeting times to be announced in the IMA schedules.

The seminars do not meet during workshops.

New Directions Visiting Professorships

The application deadline for IMA New Directions Visiting Professorships for 2006–2007 is November 1, 2005. New Directions Visiting Professorships provide an extraordinary opportunity for established mathematicians—typically mid-career faculty at US universities—to branch into a new area and increase the impact of their research by spending the 2006–2007 academic year immersed in the thematic program Applications of Algebraic Geometry. Visiting Professors will enjoy an excellent research environment and stimulating scientific program connecting algebraic geometry and related areas of mathematics with a broad range of fields of application. The New Directions program will supply 50% of academic year salary up to $50,000 maximum.

2004–2005 IMA Annual Report

The Annual Report is available at the homepage of the 2004–2005 thematic program Mathematics of Materials and Macromolecules: Multiple Scales, Disorder, and Singularities.

IMA Events

IMA Annual Program Year Workshop

Imaging from Wave Propagation

October 17-21, 2005

Organizers: Margaret Cheney (Rensselaer Polytechnic Institute), Frank Natterer (Universitaet Muenster), William W. Symes (Rice University)


This workshop seeks to bring together researchers in disparate fields that involve wave propagation, such as seismic imaging, nondestructive testing, radar imaging, medicalultrasound imaging, medical microwave imaging, etc. These fields have developed independently of each other, and researchers in different fields can scarcely communicate with each other, in spite of the fact that they are working on problems whose mathematical foundations is high-frequency analysis for wave propagation. The goal of our first workshop will be to bring researchers coming from different applications together.

Monday, October 3

11:15a-12:15pPotential Applications of Implicit Processing to Optical TomographyAlan Thomas (Clemson University)Lind Hall 409 InvPS

Tuesday, October 4

11:15a-12:15pSome entire solutions related to phase transitionsChangfeng Gui (University of Connecticut)Lind Hall 409 PS

Wednesday, October 5

10:00a-11:00aImage processingGregory J. Randall (Universidad de la Republica)EECS 5-120

Friday, October 7

1:25p-2:25pGeometrical complexity of classification problemsTin Kam Ho (Bell Labs - Lucent Technologies)Vincent Hall 570 IPS
2:30p-3:30pInvariant signaturesPeter J. Olver (University of Minnesota)TBA

Tuesday, October 11

11:15a-12:15pObject recognition and classification with limited training dataEvgeniy Bart (University of Minnesota)Lind Hall 409 PS

Wednesday, October 12

11:15a-12:15pApplications of approximation theory to imaging compression. Informal discussion.Steven Benjamin Damelin (Georgia Southern University)
Brad Lucier (Purdue University)
Lind Hall 409

Friday, October 14

1:25p-2:25pGroping in the Dark: The Past, Present, and Future of Automotive Night VisionJeff Remillad (Ford Motor Company)Vincent Hall 570 IPS

Monday, October 17

8:15a-8:45aRegistration and coffeeEE/CS 3-176 W10.17-21.05
8:45a-9:00aOpening remarksDouglas N. Arnold (University of Minnesota)EE/CS 3-180 W10.17-21.05
9:00a-9:50aA resolution theory for stable imaging in clutter George C. Papanicolaou (Stanford University)EE/CS 3-180 W10.17-21.05
9:50a-10:20aCoffee breakEE/CS 3-176 W10.17-21.05
10:20a-11:10aSparsity-driven feature-enhanced imagingMujdat Cetin (Massachusetts Institute of Technology)EE/CS 3-180 W10.17-21.05
11:10a-11:40aCoffee breakEE/CS 3-176 W10.17-21.05
11:40a-12:30pMicrowave imaging of airborne targetsBrett Borden (Naval Postgraduate School)EE/CS 3-180 W10.17-21.05
12:30p-2:30pLunch W10.17-21.05
2:30p-3:20pEstimating mechanical tissue properties with vibro-acoustography and vibrometry James F. Greenleaf (Mayo Clinic /Foundation)EE/CS 3-180 W10.17-21.05
3:20p-3:50pCoffee breakEE/CS 3-176 W10.17-21.05
3:50p-4:20pSecond Chances, a discussion period to revisit workshop topics and issues and look towards future directions.EE/CS 3-180 W10.17-21.05
4:20p-4:30pGroup photo W10.17-21.05
4:30p-6:00pReception and poster sessionLind Hall 400 W10.17-21.05
Image Reconstruction in Thermoacoustic TomographyGaik Ambartsoumian (Texas A & M University)
TBAD. Gregory Arnold (Air Force Research Laboratory)
Wave propagation in optical waveguides with imperfectionsGiulio Ciraolo (University degli Studi de Firenze)
Image Preconditioning for a SAR Image Reconstruction Algorithm for Multipath ScatteringDavid A. Garren (Science Applications International Corp. (SAIC))
Towards Effective Seismic Imaging in Anisotropic Elastic Media Murthy N. Guddati (North Carolina State University)
Nonlinear Integral Equations in Inverse Obstacle ScatteringOlha Ivanyshyn (University of Goettingen)
Uniqueness, stability and numerical methods for some inverse and ill-posed Cauchy problemsMichael Klibanov (University of North Carolina - Charlotte)
A compactly supported aproximate wavefield extrapolator for seismic imagingGary Margrave (University of Calgary)
Unique determination of the travel time from dynamic boundary measurements in anisotropic elastic mediaAnna Mazzucato (Pennsylvania State University)
Some recent developments of the analytical reconstruction techniques for inverse scattering and inverse boundary value problems in multidemensionRoman G. Novikov (University de Nantes)
Marching schemes for inverse acoustic scattering problemsFrank Wuebbeling (Universitat Munster)
Exponential radon transform inversion based on harmonic analysis of the Euclidean motion groupCan Evren Yarman (Rensselaer Polytechnic Institute)

Tuesday, October 18

8:45a-9:00aCoffeeEE/CS 3-176 W10.17-21.05
9:00a-9:50aRadar imaging from multiply scattered wavesCliff Nolan (University of Limerick)EE/CS 3-180 W10.17-21.05
9:50a-10:20aCoffee breakEE/CS 3-176 W10.17-21.05
10:20a-11:10aUsing invariant theory to obtain estimates of unknown shape and motion, and imaging moving objects in 3D from single aperture Synthetic Aperture RadarMark Stuff (General Dynamics Advanced Information Systems)EE/CS 3-180 W10.17-21.05
11:10a-11:40aCoffee breakEE/CS 3-176 W10.17-21.05
11:40a-12:30pTBARandy Moses (Ohio State University)EE/CS 3-180 W10.17-21.05
12:30p-2:30pLunch W10.17-21.05
2:30p-3:20pTheoretical and computational aspects of statistically stable adaptive coherent interferometric imaging in random mediaLiliana Borcea (Rice University)EE/CS 3-180 W10.17-21.05
3:20p-3:50pCoffee breakEE/CS 3-176 W10.17-21.05
3:50p-4:40pAppraisal analysis in geophysical inverse problem: Tool for image interpretation and survey designPartha S. Routh (Boise State University)EE/CS 3-180 W10.17-21.05
4:40p-5:10pSecond ChancesEE/CS 3-180 W10.17-21.05

Wednesday, October 19

8:45a-9:00aCoffeeEE/CS 3-176 W10.17-21.05
9:00a-9:50aTravel time tomography, boundary rigidity and electrical impedance tomography Gunther A. Uhlmann (University of Washington)EE/CS 3-180 W10.17-21.05
9:50a-10:20aCoffee breakEE/CS 3-176 W10.17-21.05
10:20a-11:10aImaging using coherently and diffusely scattered radiationJakob J. Stamnes (University of Bergen)EE/CS 3-180 W10.17-21.05
11:10a-11:40aCoffee breakEE/CS 3-176 W10.17-21.05
11:40a-12:30pTBAChris Stolk (University of Twente)EE/CS 3-180 W10.17-21.05
12:30p-2:30pLunch W10.17-21.05
2:30p-4:00pPanel discussionEE/CS 3-180 W10.17-21.05
3:20p-3:50pCoffee breakEE/CS 3-176 W10.17-21.05
4:00p-4:30pSecond ChancesEE/CS 3-180 W10.17-21.05

Thursday, October 20

8:45a-9:00aCoffeeEE/CS 3-176 W10.17-21.05
9:00a-9:50aMultiple scattering and microDoppler effects in radar imaging and target recognitionHao Ling (University of Texas - Austin)EE/CS 3-180 W10.17-21.05
9:50a-10:20aCoffee breakEE/CS 3-176 W10.17-21.05
10:20a-11:10aOn the dynamics of interbed multiplesFons Ten Kroode (Shell Research)EE/CS 3-180 W10.17-21.05
11:10a-11:40aCoffee breakEE/CS 3-176 W10.17-21.05
11:40a-12:30pA direct imaging algorithm for extended targets using active arraysHongkai Zhao (University of California - Irvine)EE/CS 3-180 W10.17-21.05
12:30p-2:30pLunch W10.17-21.05
2:30p-3:20pConvergence of products of Fourier integral operators to solutions to first-order pseudodifferential wave equations; Application to seismic imagingJerome Le Rousseau (University Aix Marseille III (Saint-Jerome))EE/CS 3-180 W10.17-21.05
3:20p-3:50pCoffee breakEE/CS 3-176 W10.17-21.05
3:50p-4:20pSecond ChancesEE/CS 3-180 W10.17-21.05
4:30p-6:00pPoster sessionLind Hall 400 W10.17-21.05
Seismic velocity analysis: in time or depth domain?Herve Chauris (Ecole des Mines de Paris)
Ultrawideband microwave breast cancer detection: beamforming for 3-D MRI-derived numerical phantomsShakti K. Davis (University of Wisconsin - Madison)
Fast, High-Order Integral Equation Methods for Scattering by Inhomogeneous MediaE. Mckay Hyde (Rice University)
Convergence rate of the iterative methods in inverse and ill-posed problemsSergey Igorevich Kabanikhin (Sobolev Institute for Mathematics)
Convergence of approximations of solutions to first-order pseudodifferential wave equations with products of Fourier integral operatorsJerome Le Rousseau (University Aix Marseille III (Saint-Jerome))
Regularization and Prior Error Distributions in Ill-posed ProblemsJodi L. Mead (Boise State University)
Imaging Cardiac Activity by the D-bar Method for Electrical Impedance TomographyJennifer Mueller (Colorado State University)
Adjoint method in time domain ultrasound tomographyFrank Natterer (Universitaet Muenster)
Iterative solver for the wave equation in the frequency domainRene-Edouard Plessix (Shell Research)
Texture discrimination, nonlinear filtering, and segmentation in mammographyWalter Richardson (University of Texas - San Antonio)
Nonlinear inverse scattering and velocity analysisWilliam W. Symes (Rice University)
A new reconstruction algorithm for Radon dataYuan Xu (University of Oregon)

Friday, October 21

8:45a-9:00aCoffeeEE/CS 3-176 W10.17-21.05
9:00a-9:50aTwo-way wave-equation migrationWim Mulder (Shell Research)EE/CS 3-180 W10.17-21.05
9:50a-10:20aCoffee break W10.17-21.05
10:20a-11:10aThe insidious effects of fine-scale heterogeneity in reflection seismologyPatrick Lailly (Institut Francais du Petrole)EE/CS 3-180 W10.17-21.05
11:10a-11:30aCoffee breakEE/CS 3-176 W10.17-21.05
11:40a-12:30pTBAAnthony J. Devaney (Northeastern University)EE/CS 3-180 W10.17-21.05
12:30p-2:30pLunch W10.17-21.05
2:30p-3:20pThe partial- approach to approximate inverse scattering at fixed energy in three dimensions.Roman G. Novikov (University de Nantes)EE/CS 3-180 W10.17-21.05
3:20p-3:50pCoffee breakEE/CS 3-176 W10.17-21.05
3:50p-4:40pAnalysis of 'wave-equation' imaging of reflection seismic data with curveletsMaarten De Hoop (Purdue University)EE/CS 3-180 W10.17-21.05
4:40p-5:10pSecond ChancesEE/CS 3-180 W10.17-21.05

Monday, October 24

11:15a-12:15pTBAAhmed Tewfik (University of Minnesota)Lind Hall 409 INvPS

Tuesday, October 25

11:15a-12:15pTBAAnne Gelb (Arizona State University)Lind Hall 409 PS

Friday, October 28

1:25p-2:25pTBAValerio Pascucci (Lawrence Livermore National Laboratories)Vincent Hall 570 IPS

Event Legend:

IPSIndustrial Problems Seminar
InvPSInverse Problems Seminar
PSIMA Postdoc Seminar
W10.17-21.05Imaging from Wave Propagation
Gaik Ambartsoumian (Texas A & M University) Image Reconstruction in Thermoacoustic Tomography
Abstract: Thermoacoustic tomography (TCT or TAT) is a new and promising method of medical imaging. It is based on a so-called hybrid imaging technique, where the input and output signals have different physical nature. In TCT a radiofrequency (RF) electromagnetic pulse is sent through the biological object triggering an acoustic wave measured on the edge of that object. The obtained data is then used to recover the RF absorption function. The poster addresses several problems of image reconstruction in thermoacoustic tomography. The presented results include injectivity properties of the related spherical Radon transform, its range description, reconstruction formulas and their implementation as well as some other results.
Evgeniy Bart (University of Minnesota) Object recognition and classification with limited training data
Abstract: Learning a visual task frequently requires a large training set, which may be costly to obtain. In this talk, we suggest an approach to reducing the required amount of training data. The approach is based on reusing experience with already learned tasks to facilitate learning the novel task. This general method is illustrated on two specific visual tasks. The first task is object recognition across variations of viewing conditions (such as viewpoint). Experience with familiar objects of a certain class (such as faces or cars) is used to facilitate generalization to previously unseen views of novel objects of the same class. In the resulting scheme, a face that has only been seen in a frontal view is successfully recognized in profile. Pose, illumination, and other viewing conditions are handled in a single general framework. The second task is object classification. The goal here is to observe a single instance of a novel class, and to generalize to additional instances of this class. Experience with already learned classes is used to facilitate this generalization. Both high-level data (on the level of entire classes) and middle-level data (on the level of individual features) help improve generalization. Combining the two sources of information further improves the performance. Joint work with Shimon Ullman.
Liliana Borcea (Rice University) Theoretical and computational aspects of statistically stable adaptive coherent interferometric imaging in random media
Abstract: jointly with George Papanicolaou (Stanford) and Chrysoula Tsogka (U. Chicago) I will discuss a robust, coherent interferometric approach for array imaging in cluttered media, in regimes with significant multipathing of the waves by the inhomogeneities in clutter. In such scattering regimes, the recorded traces at the array have long and noisy codas and classic imaging methods give unstable results. Coherent interferometry is essentially a very efficient statistical smoothing technique that exploits systematically the spatial and temporal coherence in the data to obtain stable images. I will describe in some detail the resolution of this method for two types of cluttered media: (1) isotropic, weakly scattering clutters, where waves are scattered mostly forward and (2) layered, strongly fluctuating clutters, where back scattering is strong. I will show that in spite of such opposite wave scattering regimes, coherent interferometry behaves equally well, which indicates its wide applicability. In coherent interferometry, there is a delicate balance between having stable and sharp images and achieving the optimal resolution depends on our knowledge of the clutter dependent spatial and temporal decoherence parameters. I will explain briefly how we can estimate these parameters efficiently during the image formation process, as we do in adaptive coherent interferometry.
Brett Borden (Naval Postgraduate School) Microwave imaging of airborne targets
Abstract: An important problem (perhaps the most important problem to the Department of Defense) in modern remote sensing is that of correctly identifying potential targets at great distances and in all kind of weather. Because of their ability to see through clouds and in the absence of ambient radiation, active radar systems are usually required for this task. The practical differences between ground and airborne targets allow the airborne case to focus more on actual imaging (as opposed to clutter rejection) and we will review the current methods within this simpler context. Open problems will be discussed.
Mujdat Cetin (Massachusetts Institute of Technology) Sparsity-driven feature-enhanced imaging
Abstract: We present some of our recent work on coherent image reconstruction. The primary application that has driven this work has been synthetic aperture radar, although we have extended our approach to other modalities such as ultrasound imaging as well. One of the motivations for our work has been the increased interest in using reconstructed images in automated decision-making tasks. The success of such tasks (e.g. target recognition in the case of radar) depends on how well the computed images exhibit certain features of the underlying scene. Traditional coherent image formation techniques have no explicit means to enhance features (e.g. scatterer locations, object boundaries) that may be useful for automatic interpretation. Another motivation has been the emergence of a number of applications where the scene is observed through a sparse aperture. Examples include wide-angle imaging with unmanned air vehicles (UAVs), foliage penetration radar, bistatic imaging, and passive radar imaging. When traditional image formation techniques are applied to these sparse aperture imaging problems, they often yield high sidelobes and other artifacts that make the image difficult to interpret. We have developed a mathematical foundation and associated algorithms for model-based, feature-enhanced imaging to address these challenges. Our framework is based on a regularized reconstruction of the scattering field, which combines an explicit mathematical model of the data collection process with non-quadratic functionals representing prior information about the nature of the features of interest. In particular, the prior information we exploit is that the underlying signals exhibit some form of sparsity. We solve the challenging optimization problems posed in our framework by computationally efficient numerical algorithms that we have developed. The resulting images offer improvements over conventional images in terms of visual and automatic interpretation of the underlying scenes. We also discuss a number of open research avenues inspired by this work.
Herve Chauris (Ecole des Mines de Paris) Seismic velocity analysis: in time or depth domain?
Abstract: jointly with Gilles Lambare (Ecole des Mines de Paris) Seismic velocity analysis is a crucial step needed to obtain consistent images of the subsurface. Several new methods appeared in the last 10 years, among them Slope Tomography and Differential Semblance Optimization. We want to discuss here the link between these a priori different methods. Slope Tomography is formulated in the prestack unmigrated time domain and uses not only time information picked on seismic gathers, but also associated slopes that better constrain the inversion scheme. On the other side, Differential Semblance Optimization is formulated in the depth migrated domain where adjacent images are compared to obtain a final consistent image of the subsurface. We analyse these two types of methods to show that they are in fact equivalent from a theoretical point of view despite the different formulation.
Giulio Ciraolo (University degli Studi de Firenze) Wave propagation in optical waveguides with imperfections
Abstract: The problem of electromagnetic wave propagation in a 2-D infinite optical waveguide will be presented. We give a description on how to construct a solution to the electromagnetic wave propagation problem in a 2-D and 3-D rectilinear optical waveguide. Numerical simulations will also be shown. Furthermore, in the 2-D case, we will present a mathematical framework which allows us to study waveguides with imperfections. In this case, some numerical result concerning the far field of the solution and the coupling between guided modes will be shown.
Shakti K. Davis (University of Wisconsin - Madison) Ultrawideband microwave breast cancer detection: beamforming for 3-D MRI-derived numerical phantoms
Abstract: Microwave imaging has the potential to be a highly sensitive modality for breast cancer detection due to the dielectric-properties contrast that exists between malignant and normal breast tissue at microwave frequencies. One microwave imaging approach is to transmit ultrawideband (UWB) microwave pulses into the breast, record the scattered fields, and use radar methods such as beamforming to detect and localize significant scatterers such as tumors. We previously proposed a beamforming technique and demonstrated its accuracy and robustness for tumor detection using 2-D MRI-derived numerical breast phantoms (Davis, et. al, JEMWA, 17(2):357-381, 2003) and simple 3-D physical phantoms (Li, et. al, IEEE T-MTT, 52(8):1856-1865, 2004). In this poster we extend our investigation to 3-D MRI-derived numerical breast phantoms. These anatomically realistic breast phantoms represent a prone patient with an antenna array surrounding the breast. Small (< 1 cm) tumors are added by elevating the dielectric properties in a region to represent a specified malignant-to-normal tissue contrast. We solve for backscattered fields at each antenna position using the FDTD-method and construct a 3-D image of scattered energy in the breast using our beamforming technique. The resulting images exhibit localized high-energy peaks within a few mm of the true tumor locations as expected. This work represents our first successful demonstration of detecting and localizing very small tumors in 3-D MRI-derived numerical breast models.
Maarten De Hoop (Purdue University) Analysis of 'wave-equation' imaging of reflection seismic data with curvelets
Abstract: in collaboration with Gunther Uhlmann and Hart Smith In reflection seismology one places sources and receivers on the Earth's surface. The source generates waves in the subsurface that are reflected where the medium properties vary discontinuously; these reflections are observed in all the receivers. The data thus obtained are commonly modeled by a scattering operator in a single scattering approximation: the linearization is carried out about a smooth background medium, while the scattering operator maps the (singular) medium contrast to the scattered field observation. In seismic imaging, upon applying the adjoint of the scattering operator, the data are mapped to an image of the medium contrast. We discuss how multiresolution analysis can be exploited in representing the process of `wave-equation' seismic imaging. The frame that appears naturally in this context is the one formed by curvelets. The implied multiresolution analysis yields a full-wave description of the underlying seismic inverse scattering problem on the one the hand but reveals the geometrical properties derived from the propagation of singularities on the other hand. The analysis presented here relies on the factorization of the seismic imaging process into Fourier integral operators associated with canonical transformations. The approach and analysis presented in this talk aids in the understanding of the notion of scale in the data and how it is coupled through imaging to scale in - and regularity of - the background medium. In this framework, background media of limited smoothness can be accounted for. From a computational perspective, the analysis presented here suggests an approach that requires solving for the geometry on the one hand and solving a matrix Volterra integral equation on the other hand. The Volterra equation can be solved by recursion - as in the computation of certain multiple scattering series; this process reveals the curvelet-curvelet interaction in seismic imaging. The extent of this interaction can be estimated, and is dependent on the Hölder class of the background medium.
David A. Garren (Science Applications International Corp. (SAIC)) Image Preconditioning for a SAR Image Reconstruction Algorithm for Multipath Scattering
Abstract: Recent analysis has resulted in an innovative technique for forming synthetic aperture radar (SAR) images without the multipath ghost artifacts that arise in traditional methods. This technique separates direct-scatter echoes in an image from echoes that are the result of multipath, and then maps each set of reflections to a metrically correct image space. Current processing schemes place the multipath echoes at incorrect (i.e., ghost) locations due to fundamental assumptions implicit in conventional array processing. Two desired results are achieved by use of this Image Reconstruction Algorithm for Multipath Scattering (IRAMS). First, the intensities of the ghost returns are reduced in the primary image space, thereby improving the relationship between the image pattern and the physical distribution of the scatterers. Second, a higher dimensional image space that enhances the intensities of the multipath echoes is created which offers the potential of dramatically improving target detection and identification capabilities. This paper develops techniques in order to precondition the input images at each level and each offset in the IRAMS architecture in order to reduce multipath false alarms.
James F. Greenleaf (Mayo Clinic /Foundation) Estimating mechanical tissue properties with vibro-acoustography and vibrometry
Abstract: Detecting pathology using the "stiffness" of the tissue is more that 2000 years old. Even today it is common for surgeons to feel lesions during surgery that have been missed by advanced imaging methods. Palpation is subjective and limited to individual experience and to the accessibility of the tissue region to touch. It appears that a means of noninvasively imaging elastic modulus (the ratio of applied stress to strain) may be useful to distinguish tissues and pathologic processes based on mechanical properties such as elastic modulus. The approaches to date have been to use conventional imaging methods to measure the mechanical response of tissue to mechanical stress. Static, quasi-static or cyclic stresses have been applied. The resulting strains have been measured using ultrasound or MRI and the related elastic modulus has been computed from viscoelastic models of tissue mechanics. Recently we have developed a new ultrasound technique that produces speckle free images related to both tissue stiffness and reflectivity. This method, termed "Ultrasound Stimulated Vibro-acoustography" (Science 280:82-85, April 3, 1998; Proc Natl Acad Sci USA 96:6603-6608, June 1999), uses ultrasound radiation pressure to produce sound vibrations from a small region of the tissue that depend in part on the elastic characteristics of the tissue. The method can detect micro-calcification within breasts, and promises to provide high quality images of calcification within arteries. In addition, vibro-acoustography can detect mechanical defects in certain prostheses such as artificial mitral and aortic valves. Extensions of the method include vibrometry, in which motion of an object is detected with laser vibrometry or an accelerometer, and shear wave detection, in which the resulting shear waves within objects such as arteries or tissue are detected with Doppler or MRI. Keywords : vibrometry, stiffness, ultrasound, acoustic, shear waves
Murthy N. Guddati (North Carolina State University) Towards Effective Seismic Imaging in Anisotropic Elastic Media
Abstract: [joint work with A.H. Heidari] A critical ingredient in high-frequency imaging is the migration operator that back-propagates the surface response to the hidden reflectors. Migration is often performed using one-way wave equations (OWWEs) that allow wave propagation in a preferred direction while suppressing the propagation in the opposite direction. OWWEs are typically obtained by approximating the factorized full-wave equation; this process is well-developed for the acoustic wave equation, but not for elastic wave equations, especially when the material is anisotropic. Furthermore, existing elastic OWWEs are computationally expensive. For these reasons, in spite of the existence of strongly coupled elastic waves, seismic migration is performed routinely using acoustic OWWEs, naturally resulting in significant errors in the image. With the ultimate goal of developing accurate and efficient imaging algorithms for anisotropic elastic media, we develop new approximations of elastic OWWEs. Named the arbitrarily wide-angle wave equations (AWWEs), these approximations appear to be effective for isotropic as well as anisotropic media. The implementation of AWWE-migration in isotropic (heterogeneous) elastic media is complete, while further work remains to be done to incorporate the effects of anisotropy. This poster outlines (a) the basic idea behind AWWEs, (b) the implementation of AWWE-migration along with some results, and (c) future challenges related to using AWWEs for imaging in anisotropic elastic media.
E. Mckay Hyde (Rice University) Fast, High-Order Integral Equation Methods for Scattering by Inhomogeneous Media
Abstract: Integral equation methods for the time-harmonic scattering problem are attractive since the radiation condition at infinity is automatically satisfied (no absorbing boundary condition is required), only the scattering obstacle itself needs to be discretized, and the integral operator is compact, leading to better conditioned linear systems than for differential operators. However, there has been limited success in developing integral equation methods which are both efficient and high-order accurate. We will present recent work on integral equation methods that are both efficient (O(N log N) complexity) and high-order accurate in computing the time-harmonic scattering by inhomogeneous media. The efficiency of our methods relies on the use of fast Fourier transforms (FFTs) while the high-order accuracy results from systematic use of partitions of unity, regularizing changes of variables, and Fourier smoothing of the refractive index.
Olha Ivanyshyn (University of Goettingen) Nonlinear Integral Equations in Inverse Obstacle Scattering
Abstract: We present a novel solution method for inverse obstacle scattering problems for time-harmonic waves based on a pair of nonlinear and ill-posed integral equations for the unknown boundary that arises from the reciprocity gap principle. This integral equations can be solved by linearization, i.e., by regularized Newton iterations. We present a mathematical foundation of the method and illustrate its feasibility by numerical examples.
Sergey Igorevich Kabanikhin (Sobolev Institute for Mathematics) Convergence rate of the iterative methods in inverse and ill-posed problems
Abstract: The rate of convergence for Newton-type and gradient mehtods is discussed for several examples of inverse and ill-posed problems, such as inverse acoustic problem, Cauchy problem for Laplace equation, ill-posed Cauchy problems for parabolic equation.
Tin Kam Ho (Bell Labs - Lucent Technologies) Geometrical complexity of classification problems
Abstract: Pattern recognition seeks to identify and model regularities in empirical data by algorithmic processes. Successful application of the established methods requires good understanding of their behavior and also how well they match the application context. Difficulties can arise from either the intrinsic complexity of a problem or a mismatch of methods to problems. We describe some measures that can characterize the intrinsic complexity of a classification problem and its relationship to classifier performance. The measures revealed that a collection of real-world problems can span an interesting continuum between those easily learnable to those with no learning possible. We discuss our results on identifying the domains of dominant competence of several popular classifiers in this measurement space.
Michael Klibanov (University of North Carolina - Charlotte) Uniqueness, stability and numerical methods for some inverse and ill-posed Cauchy problems
Abstract: Some new results concerning global uniqueness theorems and stability estimates for coefficient inverse problems will be presented. In addition, the presentation will cover some new and previous results about the stability of the Cauchy problem for hyperbolic equations with the data at the lateral surface. This problem is almost equivalent with the inverse problem of determining initial conditions in hyperbolic equations. Therefore, stability estimates for this Cauchy problem actually imply refocusing of time reversed wave fields. Our recent numerical studies confirming this statement will be presented. In addition, a globally convergent algorithm for a class of coefficient inverse problems will be discussed. The main tool of all these studies is the method of Carleman estimates.
Patrick Lailly (Institut Francais du Petrole) The insidious effects of fine-scale heterogeneity in reflection seismology
Abstract: Joint work with Florence Delprat-Jannaud. Geophysicists are quite aware of the important troubles that can be met when the seismic data are contaminated by multiple reflections. The situation they have in mind is the one where multiple reflections are generated by isolated interfaces associated with high impedance contrasts. We here study a more insidious effect of multiple scattering, namely the one associated with fine scale heterogeneity. Our numerical experiments show that the effect of such multiple scattering can be far from negligible. As a consequence, it can lead standard imaging techniques (based on high-frequency analysis for wave propagation) to complete failure. The parameters that control the importance of the phenomenon are the depth of the target and the heterogeneity of the overburden. The dynamic theory of homogenization, unfortunately available only in 1D, allows us to better understand the role of the seismic frequency band: the multiple scattering phenomenon is all the more important as we deal with high frequencies. This leads to an interesting consequence: we can take advantage of a super-resolution phenomenon; namely, in situations where multiple scattering is important, we can expect a higher resolution than the one given by the classical Rayleigh criterion. References Delprat-Jannaud, F. and Lailly, P., 2004. The insidious effects of fine-scale heterogeneity in reflection seismology. Journal of Seismic Exploration, 13: 39-84. Bamberger, A., Chavent, B. and Lailly, P., 1979. About the stability of the inverse problem in the 1D wave equation, application to the interpretation of seismic profiles, Journal of Applied Mathematics and Optimization, 5: 1-47.
Jerome Le Rousseau (University Aix Marseille III (Saint-Jerome)) Convergence of approximations of solutions to first-order pseudodifferential wave equations with products of Fourier integral operators
Abstract: An approximation of the solution to a hyperbolic equation with a damping term is introduced. It is built as the composition of Fourier integral operators (FIO). We prove the convergence of this approximation in the sense of Sobolev norms as well as for the wavefront set of the solution. We apply the introduced method to numerically image seismic data.
Hao Ling (University of Texas - Austin) Multiple scattering and microDoppler effects in radar imaging and target recognition
Abstract: Synthetic aperture radar (SAR) and inverse synthetic aperture radar (ISAR) systems have long been used by the radar community for imaging air, sea and ground targets. The standard radar imaging algorithms used in these systems are based on the single-scattering, point-scatterer model of the target. When the actual target scattering is well approximated by this simple model, the resulting high-resolution imagery reveals useful geometrical features of the target for classification and identification. However, sensor data collected from real targets often contain higher order effects. For instance, strong multiple scattering can occur in a real target with reentrant structures and inlet cavities. Further, a real target being imaged by a radar sensor is often engaged in dynamic maneuvers where the target does not remain a rigid body. Some examples include the flexing and vibration of the target frame and moving parts on the target such as scanning antennas, moving wheels and treads. These motions give rise to Doppler features after the standard radar processing and have been referred to as the microDoppler phenomenon. When these higher order effects are present, the resulting target imagery contains artifacts due to the mismatch between the imaging model and the actual data. More importantly, these features contain useful information about the motion of the moving components and the interior characteristics of the target, and should be better exploited for target recognition. In this talk, I will discuss our ongoing research in: (i) the extraction, understanding and modeling of these phenomena, and (ii) the exploitation of the resulting models to achieve better imaging and recognition performance.
Gary Margrave (University of Calgary) A compactly supported aproximate wavefield extrapolator for seismic imaging
Abstract: Seismic imaging in highly heterogeneous media requires an adaptive, robust, and efficient wavefield extrapolator. The homgeneous medium wavefield extrapolator has no spatial adaptivity but the locally homogeneous approximate extrapolator (LHA) is a highly accurate Fourier integral operator that adapts rapidly in space. Efficient application of either wavefield extrapolator is complicated by the fact that they have impulse responses that are not compactly supported, though they decay rapidly. Simple locaization methods, such as windowing, result in compactly supported approximations that are unstable in a recursive marching scheme. I present an analysis of this instability effect and a localization scheme that can design compactly supported approximate extrapolators that are sufficiently stable for hundreds of marching steps. I illustrate the method with seismic images from the Marmousi synthetic dataset.
Anna Mazzucato (Pennsylvania State University) Unique determination of the travel time from dynamic boundary measurements in anisotropic elastic media
Abstract: We microlocally decouple the system of equations for anisotropic elastodynamics (in 3 dimensions) following a result of M. Taylor. We then show that the dynamic Dirichlet-to-Neumann map uniquely determines the travel time through a bounded elastic body for any wave mode that has disjoint light cone. We apply this result to cases of transversely isotropic media with rays that are geodesics with respect to Riemannian metrics, and conclude that certain material parameters are uniquely determined up to diffeomorphisms that fix the boundary. We have shown that material parameters of general anisotropic elastic media may be uniquely determined by the Dirichlet-to-Neumann map only up to pullback by diffeomorphisms fixing the boundary.
Jodi L. Mead (Boise State University) Regularization and Prior Error Distributions in Ill-posed Problems
Abstract: We will examine the validity of parameter estimates in ill-posed problems when errors in data and initial parameter estimates are from normal and non-normal distributions. Given appropriate initial parameter estimates and the data error covariance matrix, the covariance matrix for errors in initial parameter estimates can be recovered and highly accurate parameter estimates can be found. This approach allows the regularization to be varied with each parameter.
Jennifer Mueller (Colorado State University) Imaging Cardiac Activity by the D-bar Method for Electrical Impedance Tomography
Abstract: Electrical Impedance Tomography (EIT) is an imaging technique that uses the propagation of electromagnetic waves through a medium to form an image. In medical EIT, current is applied through electrodes on the surface of the body, the resulting voltages are measured on the electrodes, and the inverse conductivity problem is solved numerically to reconstruct the conductivity distribution in the interior. Here results are shown from EIT data taken on electrodes placed around the circumference of a human chest to reconstruct a 2-D cross-section of the torso. The images show changes in conductivity during a cardiac cycle made from the D-bar reconstruction algorithm based on the 1996 uniqueness proof of A. Nachman [Ann.Math. 143].
Wim Mulder (Shell Research) Two-way wave-equation migration
Abstract: Joint with R.-E. Plessix. The goal of seismic surveying is the determination of the structure and properties of the subsurface. Oil and gas exploration is restricted to the upper 5 to 10 kilometers. Seismic data are usually recorded at the earth's surface as a function of time. Creating a subsurface image from these data is called migration. Seismic data are band-limited with frequencies in the range from about 10 to 60 Hz. As a result, they are mainly generated by short-range variations in the subsurface impedance, the product of velocity and density. The common approach towards migration is the construction of a reflection-free background velocity model from the apparent travel times from source to receiver. In this background model, the migration algorithm maps the data amplitudes to the impedance contrasts that generated them. Single scattering is implicitly assumed. The wave propagation in the background model is usually described by an approximation to the wave equation to keep the required computer time down to months. Ray tracing used to be a popular choice, but is gradually taken over by one-way (paraxial or parabolic) wave equation approximations. We have investigated the use of the acoustic wave equation, which will we call the two-way wave equation in order to distinguish it from the widely used one-way wave equation. The two-way approach provides a more accurate description of wave propagation than the one-way method, particularly near underground structures that have steep interfaces. The one-way equation requires considerably less computer time in 3D, but in 2D the one-way and two-way methods compete. Migration algorithms can be derived from the least-squares error that measures the difference between observed and modeled data. The gradient of this functional with respect to the model parameters is a migration image. This gradient can be used to minimize the error, but leads to a problem that is nonlinear in the model parameters and has many local minima. Gradient-based optimization algorithms will only provide meaningful results if the initial model is close to the global minimum. Because migration is computational very costly, global searches are not an option. An alternative is to return to the classic approach, where migration serves to map the impedance contrasts without changing the wave propagation model. This can be achieved in the context of the two-way wave equation by assuming that the contrasts are small perturbations, leading to a linearization with respect to the model parameters. This is the well-known Born approximation. A disadvantage of the two-way method is that it models all waves, not only reflections. This may produce artifacts in the images. We will discuss ways to remove them. In the nonlinear approach, these artifacts can actually be used to update the background model. Also, multiple reflections can be included in the minimization. In general, however, the least-squares functional is not very well suited to determine the background model and an alternative cost functional needs to be sought. Examples on synthetic and real data will serve as illustrations.
Frank Natterer (Universitaet Muenster) Adjoint method in time domain ultrasound tomography
Abstract: We model ultrasound tomography by the wave equation. Adjoint methods can be used for the inversion. Unfortunately, due to the large number of sources, adjoint methods are very time consuming. By preprocessing of the data (wavefront synthesizing, plane wave stacking), adjoint methods can be sped up by orders of magnitude. We analyse the preprocessed data in Fourier domain. We present numerical results for the Salt Lake City breast phantom and for the Marmousi data.
Cliff Nolan (University of Limerick) Radar imaging from multiply scattered waves
Abstract: We consider imaging the earth's topography using synthetic aperture RADAR (SAR), as well as real aperture RADAR (RAR). We use a simple scalar wave model for the radio waves. Instead of the common approach of singly-scattered waves, we consider the situation where a reflecting 'wall' is located in the vicinity of the region of interest (ROI). We will show how it is possible to take advantage of scattering between the wall and object(s) in the ROI to improve on the convention imaging methods. An obvious benefit of such a situation is the improved angular resolution available from this kind of data. Our approach is based on microlocal analysis, which is often considered an opaque subject area to the uninitiated. However, the simplicity of the experimental set up in SAR and RAR makes for a very straightforward application of microlocal tools.
Roman G. Novikov (University de Nantes) The partial- approach to approximate inverse scattering at fixed energy in three dimensions.
Abstract: See pdf file.
George C. Papanicolaou (Stanford University) A resolution theory for stable imaging in clutter
Abstract: I will present a qualitative, model free theory for imaging in clutter with coherent interferometry. Coherent interferometry is a smoothed form of Kirchhoff or travel time migration that is implemented adaptively in order to optimize the bias-variance tradeoff in the image quality, as it is being formed. I will show the results of numerical simulations that illustrate the theory. This is joint work with L. Borcea and C. Tsogka.
Rene-Edouard Plessix (Shell Research) Iterative solver for the wave equation in the frequency domain
Abstract: Joint work with Wim Mulder. To retrieve the long and short spatial frequencies of the velocity model from seismic data, several authors have proposed to work in the frequency-domain. The data are inverted per frequency going from the low to the high. This approach has been used for long offset data in two dimensional space. It relies on the solution of the wave equation in the frequency domain (Helmholtz equation). Whereas in two dimensional space, a direct solver of the frequency-domain wave equation provides an efficient method, in three dimensional space, this approach is not feasible because the linear system becomes too large. This difficulty may be overcome with an iterative solver for the Helmholtz equation. During his Ph. D work, Y. Erlangga has studied an iterative approach based on a preconditioned bicgstab (conjugate-gradient type) method. The efficiency of the method depends on the preconditioner. It was proposed to use a damped wave equation as a preconditioner and to approximate the inverse of the damped equation with a multigrid method. Strong damping is required for the preconditioner, otherwise the multigrid method does not convergence. Two-dimensional examples show that this approach is robust and that the number of iterations depends linearly on the frequency when the number of grid points per wavelength is kept constant. Thus, this approach provides a sub-optimal solution. In the poster, several numerical examples will be presented to assess the efficiency of the iterative approach. Its relevance for migration in two and three dimensions and for inversion algorithms will also be discussed.
Gregory J. Randall (Universidad de la Republica) Image processing
Abstract: In this talk I will present a general overview of the work in my group, the GTI (Image Processing Group) at the Electrical Engineering Department, Universidad de la Republica, Uruguay.

The GTI does research, teaching and consulting in image processing. We are currently responsible of several undergraduate and posgraduate courses and research projects. Our goal is to apply these techniques in order to contribute to solve problems of national interest (in the context of a little third world country), and doing so, to generate a local critical mass of peopple working in this field. I think that in this 11 years effort we have some interesting outputs.

The principal applications in which the GTI has worked are:
Applications to biology and medicine.
Applications to the productive sector.

Image processing problems of interest:
3D reconstruction and visualization.

Jeff Remillad (Ford Motor Company) Groping in the Dark: The Past, Present, and Future of Automotive Night Vision
Abstract: Night vision was first introduced into the automotive market 5 years ago on the Cadillac DeVille, and then 2 years later on the Lexus LX 470 sport-utility-vehicle. In spite of initial consumer interest, Cadillac no longer offers this feature, and in general, night-vision has failed to generate significant interest in the marketplace. However, Honda has introduced a night-vision system based on the use of two thermal-cameras that also provides a pedestrian detection function, and BMW and DCX will be launching a night-vision option within the next year on the 7-Series, and S-Class, respectively. Which, if any, of these products will capture the imagination of the driving public, and what night-vision technology/feature package offers the best performance and business case? This talk will compare and contrast various approaches to automotive night vision, and specifically describe the laser-based system developed by Ford, which consists of a laser illuminator and CCD camera that are located in the vehicle interior. In contrast to thermal night vision technologies, it provides easily recognizable images of both pedestrians and inanimate objects and in contrast to the active-night-vision system offered by Lexus, it provides clear imagery even in the presence of oncoming traffic. The talk will also describe a prototype range-gated laser-based night-vision-system that enables viewing through snow, fog, and other obscurants.
Walter Richardson (University of Texas - San Antonio) Texture discrimination, nonlinear filtering, and segmentation in mammography
Abstract: There are two primary signs used by the radiologist to detect lesions. The first is mass: a benign neoplasm is smoothly marginated whereas a malignancy is characterized by an indistinct border which becomes more spiculated with time. The second sign is microcalcification. An essential ingredient of these indicators is texture, used by the radiologist in many subtle ways to discriminate between normal and cancerous tissue. The irregular boundaries of suspect lesions suggest that they could be identified by their local fractal signature. Any real image is corrupted by some noise and it is necessary to prefilter the data. Results are presented for two edge-enhancing filters: the Weighted Majority - Minimum Range filter and the mean-curvature dependent PDE filter of Morel. Once the image has been filtered/transformed, the Mumford-Shah approach is used for segmentation.
Partha S. Routh (Boise State University) Appraisal analysis in geophysical inverse problem: Tool for image interpretation and survey design
Abstract: Joint work with Doug Oldenburg. Image appraisal in geophysical inverse problem can provide insight into the resolving capability and uncertainty of estimates. Although a rigorous approach to solve nonlinear appraisal analysis is still lacking but several methods have been proposed in the past such as linearized Backus-Gilbert analysis, funnel function method and nonlinear Backus-Gilbert formulation where forward problem can be expressed as scattering series. In this talk I will discuss appraisal analysis and how it can be used for image interpretation and survey design. In image interpretation the goal is to quantify what part of model can be resolved by the data and what parts are consequence of regularization operator? In survey design the objective is to determine optimal survey parameters, such as the position of sources/receivers and possibly frequencies in EM experiments, that would provide better' model resolution in a region of interest. For both of these problems we examine the resolution measure called point spread function. The point spread function quantifies how an impulse in the true model is observed in the inversion result and, hence, the goal is to adjust the survey parameters so that the point spread function is as delta-like as possible. This problem is solved as a nonlinear optimization problem with constraints on the parameters. Examples from ray-based tomography and controlled source electromagnetics will be presented.
Jakob J. Stamnes (University of Bergen) Imaging using coherently and diffusely scattered radiation
Abstract: The talk will be divided in two parts. The first part will be devoted to diffraction tomography based on the scalar wave equation to obtain images of the refractive-index distribution of an object embedded in a homogeneous medium, with emphasis on experimental verifications of this technique in applications using light or ultrasound. The second part of the talk will be devoted to imaging of objects embedded in turbid media, based on radiative transfer theory. Here the emphasis will be on passive optical remote sensing from satellite for identifying and mapping algae distributions in the ocean, as well as on the use of light for diagnosis of skin abnormalities, such as skin cancer.
Mark Stuff (General Dynamics Advanced Information Systems) Using invariant theory to obtain estimates of unknown shape and motion, and imaging moving objects in 3D from single aperture Synthetic Aperture Radar
Abstract: When a moving object is imaged with conventional synthetic aperture radar (SAR) the result is a displaced smear. This is due to the extra information the objectmotion is imparting to the radar return. When a sensor collects data from a moving extended object, estimation of the direction vectors from the object to the sensor is often essential to the extraction of useful information from the sensor data. If the object or the sensor moves as result of uncontrolled or unknown forces, simple parametric models for the angular motions often rapidly loose fidelity. So, even if the object can be modeled parametrically, nonparametric motion estimates are desirable. In one example of such a problem, a direct approach to estimating all the unknowns leads to difficult nonlinear optimization problems. But a characterization of the shape of the object, using the right choice of geometric invariants, can decouple the problem, temporarily isolating the object shape estimation from the motion estimation. This facilitates the extraction of nonparametric motion estimates both by subdividing the parameter space, and by enabling parts of the problem to be solved using linear methods. If the motion is rich enough there should be a possibility of forming a 3D image of the object. This involves understanding the way the radar data is arranged in phase space. The data lies on a convoluted surface that occupies three dimensions rather than the two dimensional plane used in conventional SAR. To achieve three dimensional images the data must be extrapolated from the surface into a volume. In this complex space, there is a great deal of structure and therefore the possibility of extrapolating to a volume of data.
William W. Symes (Rice University) Nonlinear inverse scattering and velocity analysis
Abstract: Migration velocity analysis ("MVA") can be viewed as a solution method for the linearized ("Born") inverse scattering problem, in its reflection seismic incarnation. MVA is limited by the single scattering assumption - for example, it misinterprets multiply scattered waves - but it is capable of making large changes in the model, and moving estimated locations of scatterers by many wavelengths. The salient features of MVA is its use of an extended (nonphysical) scattering model. Nonlinear least squares inversion ("NLS"), on the other hand, incorporates whatever details of wave physics are built into its underlying modeling engine. However success appears to require that the initial estimate of wave velocity (in an iterative solution method) be "accurate to within a wavelength", i.e. have kinematic properties very close to that of the optimal model. This poster will describe a nonlinear extended scattering model and a related optimization formulation of inverse scattering. I will present the results of some preliminary numerical explorations which suggest that this approach may combine the global nature of MVA with the capacity of NLS to accomodate nonlinear wave phenomena.
Fons Ten Kroode (Shell Research) On the dynamics of interbed multiples
Abstract: Interbed multiples form a class of multiples in seismic data characterized by the property that all reflection points lie in the subsurface. This sets them apart from surface multiples, which have at least one reflection point at the surface of the earth. For surface multiples there is a well established procedure to predict them from the data, i.e. without any a-priori knowledge of the subsurface. This procedure is firmly based on the wave equation and is exact from a theoretical point of view. For interbed multiples the situation is much less satisfactory. In 1997 Art Weglein published an algorithm to predict them from the data. This algorithm is clearly a generalization of the surface related case, but its derivation is not. In fact, the algorithm initially came without a formal proof. I have tried to fill that gap in a 2001 paper, by providing a derivation based on weak scattering and asymptotics. This derivation demonstrated that the kinematics of Wegleinxs algorithm are correct, but at the same time left open the question of the dynamics. Since then I have obtained results for the dynamics by replacing the weak scattering assumption by the Kirchhoff scattering assumption. In the presentation I will explain how to obtain prediction algorithms for interbed multiples under the weak scattering and Kirchhoff scattering assumptions.
Alan Thomas (Clemson University) Potential Applications of Implicit Processing to Optical Tomography
Abstract: We will give an overview of the inverse problem in optical tomography with some common reconstruction schemes. We will follow with some ideas for potential reconstruction algorithms that utilize implicit processing. This talk is intended to stimulate a discussion between experts in image processing and those working in inverse problems.
Gunther A. Uhlmann (University of Washington) Travel time tomography, boundary rigidity and electrical impedance tomography
Abstract: In inverse boundary problems one attempts to determine the properties of a medium by making measurements at the boundary of the medium. In the lecture we will concentrate on two inverse boundary problems, Electrical Impedance Tomography and Travel Tomography in anisotropic media. These problems arise in medical imaging, geophysics and other fields. We will also discuss a surprising connection between these two inverse problems. Travel Time Tomography, consists in determining the index of refraction or sound speed of a medium by measuring the travel times of waves going through the medium. In differential geometry this is known as the the boundary rigidity problem. In this case the information is encoded in the boundary distance function which measures the lengths of geodesics joining points of the boundary of a compact Riemannian manifold with boundary. The inverse boundary problem consists in determining the Riemannian metric from the boundary distance function. Calderön's inverse boundary problem consists in determining the electrical conductivity inside a body by making voltage and current measurements at the boundary. This inverse problem is also called Electrical Impedance Tomography (EIT). The boundary information is Calderön's inverse boundary problem consists in determining the electrical conductivity inside a body by making voltage and current measurements at the boundary. This inverse problem is also called Electrical Impedance Tomography (EIT). The boundary information is encoded in the Dirichlet-to-Neumann (DN) map and the inverse problem is to determine the coefficients of the conductivity equation (an elliptic partial differential equation) knowing the DN map. A connection between these two inverse problems has led to a solution of the boundary rigidity problem in two dimensions for simple Riemannian metrics. We will also discuss a reconstruction method in two dimensions for the sound speed from first arrival times of waves.
Frank Wuebbeling (Universitat Munster) Marching schemes for inverse acoustic scattering problems
Abstract: The solution of time-harmonic inverse scattering problems usually involves solving the Helmholtz equation many times. On the other hand, these boundary value problems with radiation condition at infinity are notoriously hard to solve. In the context of inverse scattering, however, boundary value problems can be rewritten as initial value problems. We develop an efficient marching scheme for computing a filtered version of the solution of the initial value problem for the Helmholtz equation in 2D and 3D. Stability and error estimates are developped, a numerical example is given.
Yuan Xu (University of Oregon) A new reconstruction algorithm for Radon data
Abstract: A new reconstruction algorithm for Radon data is introduced. We call the new algorithm OPED as it is based on Orthogonal Polynomial Expansion on the Disk. OPED is fundamentally different from the filtered back projection (FBP) method. It allows one to use fan geometry directly without the additional procedures such as interpolation or rebinning. It reconstructs high degree polynomials exactly and converges unifomly for smooth functions without the assumption that functions are band-limited. Our initial test indicates that the algorithm is stable, provides high resolution images, and has a small global error. Working with the geometry specified by the algorithm and a new mask, OPED could also lead to a reconstruction method working with reduced x-ray dose.
Can Evren Yarman (Rensselaer Polytechnic Institute) Exponential radon transform inversion based on harmonic analysis of the Euclidean motion group
Abstract: This paper presents a new method for the exponential Radon transform inversion based on harmonic analysis of the Euclidean motion group (M(2)). The exponential Radon transform is modified to be formulated as a convolution over M(2). The convolution representation leads to a block diagonalization of the modified exponential Radon transform in the Euclidean motion group Fourier domain, which provides a deconvolution type inversion for the exponential Radon transform. Numerical examples are presented to show the viability of the proposed method.
Hongkai Zhao (University of California - Irvine) A direct imaging algorithm for extended targets using active arrays
Abstract: We present a direct imaging algorithm for both the location and geometry of extended targets. Our algorithm is based on a physical factorization of the response matrix of an active array. A resolution and noise level based thresholding is used for regularization. Our algorithm is extremely simple and efficient since no forward solver or iterations are needed. Multiple-frequencies can be used to improve the stability of our algorithm. We demonstrate the efficiency and roubustness with respect to both measurement noise and random background.
Visitors in Residence
Tuncay Aktosun University of Texas at Arlington 10/16/2005 - 10/22/2005
Gaik Ambartsoumian Texas A & M University 10/16/2005 - 10/22/2005
Jung-Ha An University of Minnesota 9/1/2005 - 8/31/2007
John M. M. Anderson Howard University 10/16/2005 - 10/21/2005
Fredrik Andersson Lund University 9/17/2005 - 11/14/2005
Michael Andre University of California - San Diego 10/16/2005 - 10/21/2005
D. Gregory Arnold Air Force Research Laboratory 10/17/2005 - 10/20/2005
Douglas N. Arnold University of Minnesota 7/15/2001 - 8/31/2006
Donald G. Aronson University of Minnesota 9/1/2002 - 8/31/2006
Gang Bao Michigan State University 10/16/2005 - 10/21/2005
Paul E. Barbone Boston University 10/16/2005 - 10/22/2005
Evgeniy Bart University of Minnesota 9/1/2005 - 8/31/2007
Francisco Blanco-Silva Purdue University 9/1/2005 - 6/30/2006
Bob Bonneau Air Force Research Laboratory 10/16/2005 - 10/21/2005
Liliana Borcea Rice University 10/16/2005 - 10/21/2005
Brett Borden Naval Postgraduate School 10/1/2005 - 12/31/2005
David Brady Duke University 9/18/2005 - 12/10/2005
Michael P. Brenner Harvard University 10/9/2005 - 10/10/2005
Robert Burridge Massachusetts Institute of Technology 9/1/2005 - 12/31/2005
Fioralba Cakoni University of Delaware 10/16/2005 - 10/22/2005
Mujdat Cetin Massachusetts Institute of Technology 10/15/2005 - 10/22/2005
Herve Chauris Ecole des Mines de Paris 10/16/2005 - 10/21/2005
Qianyong Chen University of Minnesota 9/1/2004 - 8/31/2006
Margaret Cheney Rensselaer Polytechnic Institute 9/6/2005 - 12/31/2005
Eric Chung University of California - Irvine 10/17/2005 - 10/21/2005
Giulio Ciraolo University degli Studi de Firenze 9/8/2005 - 12/23/2005
Dana Clahane University of California - Riverside 9/18/2005 - 11/18/2005
David L. Colton University of Delaware 10/16/2005 - 10/22/2005
L. Pamela Cook University of Delaware 10/8/2005 - 10/10/2005
Steven Benjamin Damelin Georgia Southern University 8/9/2005 - 6/30/2006
Shakti K. Davis University of Wisconsin - Madison 10/16/2005 - 10/22/2005
Maarten De Hoop Purdue University 10/15/2005 - 10/31/2005
Anthony J. Devaney Northeastern University 9/5/2005 - 12/30/2005
Thomas A. Dickens ExxonMobil 10/16/2005 - 10/21/2005
Brian DiDonna University of Minnesota 9/1/2004 - 8/31/2006
Charles Doering University of Michigan 10/9/2005 - 10/10/2005
Thomas Dowling University of Limerick 10/15/2005 - 10/22/2005
Katherine B. Ensor Rice University 10/8/2005 - 10/10/2005
Yi Fang Rensselaer Polytechnic Institute 9/12/2005 - 12/20/2005
Adel Faridani Oregon State University 9/18/2005 - 10/21/2005
Raluca Felea Rochester Institute of Technology 10/16/2005 - 10/22/2005
Romina Gaburro University of Limerick 10/14/2005 - 10/23/2005
David A. Garren Science Applications International Corp. (SAIC) 10/16/2005 - 10/21/2005
Anne Gelb Arizona State University 10/10/2005 - 10/28/2005
Allan Greenleaf University of Rochester 10/16/2005 - 10/21/2005
James F. Greenleaf Mayo Clinic /Foundation 10/16/2005 - 10/21/2005
F. Alberto Grunbaum University of California - Berkeley 10/16/2005 - 10/21/2005
Murthy N. Guddati North Carolina State University 10/16/2005 - 10/21/2005
Changfeng Gui University of Connecticut 9/12/2005 - 6/30/2006
Jooyoung Hahn KAIST 8/26/2005 - 7/31/2006
Gloria Haro Ortega University of Minnesota 9/1/2005 - 8/31/2007
Scott Hensley California Institute of Technology 10/16/2005 - 10/21/2005
Thorsten Hohage George August University Goettingen 10/15/2005 - 10/22/2005
Songming Hou Michigan State University 10/17/2005 - 10/21/2005
Kai Huang University of California - Irvine 10/16/2005 - 10/22/2005
Xiang Huang University of Connecticut 9/1/2005 - 6/30/2006
E. Mckay Hyde Rice University 10/16/2005 - 10/20/2005
Olha Ivanyshyn University of Goettingen 10/16/2005 - 10/23/2005
Sookyung Joo University of Minnesota 9/1/2004 - 8/31/2006
Gerald Kaiser University of Texas - Austin 10/16/2005 - 10/22/2005
Tin Kam Ho Bell Labs - Lucent Technologies 10/6/2005 - 10/7/2005
Chiu Yen Kao University of Minnesota 9/1/2004 - 8/31/2006
Hans Kaper National Science Foundation 10/9/2005 - 10/10/2005
Mercedeh Khajavikhan University of Minnesota 10/16/2005 - 10/21/2005
Taufiquar Khan Clemson University 9/4/2005 - 12/31/2005
Michael Klibanov University of North Carolina - Charlotte 10/16/2005 - 10/21/2005
Robert V. Kohn New York University 10/8/2005 - 10/10/2005
Matthias Kurzke University of Minnesota 9/1/2004 - 8/31/2006
Song-Hwa Kwon University of Minnesota 8/30/2005 - 8/31/2007
Patrick Lailly Institut Francais du Petrole 10/16/2005 - 10/21/2005
Chang-Ock Lee KAIST 8/1/2005 - 7/31/2006
Sungyun Lee Korea Advanced Institute of Science & Technology 10/16/2005 - 10/21/2005
Ricardo Leiderman Boston University 10/16/2005 - 10/22/2005
Jerome Le Rousseau University Aix Marseille III (Saint-Jerome) 10/15/2005 - 10/30/2005
Debra Lewis University of Minnesota 7/15/2004 - 8/31/2006
Matthew A. Lewis University of Texas Southwestern Medical Center 10/16/2005 - 10/22/2005
Hstau Liao University of Minnesota 9/2/2005 - 8/31/2007
Hao Ling University of Texas - Austin 10/16/2005 - 10/21/2005
Brad Lucier Purdue University 8/15/2005 - 6/30/2006
Russell Luke University of Delaware 9/6/2005 - 12/31/2005
Peter Maass University of Bremen 9/27/2005 - 10/12/2005
Alison Malcolm University of Minnesota 9/1/2005 - 8/31/2007
Nick Marechal Aerospace Corporation 10/16/2005 - 10/21/2005
Gary Margrave University of Calgary 10/2/2005 - 10/30/2005
Anna Mazzucato Pennsylvania State University 10/16/2005 - 10/21/2005
Joyce Mclaughlin Rensselaer Polytechnic Institute 10/16/2005 - 10/28/2005
Jodi L. Mead Boise State University 10/16/2005 - 10/21/2005
Kai Medville University of Minnesota 9/1/2005 - 8/31/2007
Steen Moeller University of Minnesota 10/17/2005 - 10/21/2005
Scott Morton Amerada Hess Corporation 10/16/2005 - 10/21/2005
Randy Moses Ohio State University 10/16/2005 - 10/21/2005
Jennifer Mueller Colorado State University 10/16/2005 - 10/22/2005
Wim Mulder Shell Research 10/16/2005 - 10/21/2005
Arje Nachman AFOSR/NM 10/16/2005 - 10/22/2005
Assaf Naor Microsoft Research 9/28/2005 - 10/1/2005
Frank Natterer Universitaet Muenster 9/26/2005 - 10/22/2005
Cliff Nolan University of Limerick 10/15/2005 - 10/22/2005
Roman G. Novikov University de Nantes 10/16/2005 - 10/22/2005
Ozan Oktem Sidec Technologies AB 10/16/2005 - 10/22/2005
Peter J. Olver University of Minnesota 9/1/2005 - 6/30/2006
Miao-Jung Yvonne Ou University of Central Florida 10/18/2005 - 10/21/2005
Winston Ou University of Minnesota 9/1/2005 - 1/13/2006
Victor Palamodov Tel Aviv University 10/11/2005 - 11/30/2006
George C. Papanicolaou Stanford University 10/16/2005 - 10/22/2005
Valerio Pascucci Lawrence Livermore National Laboratories 10/27/2005 - 10/28/2005
Sarah K. Patch General Electric 10/16/2005 - 11/19/2005
Peter Philip University of Minnesota 8/22/2004 - 8/31/2006
Rene-Edouard Plessix Shell Research 10/16/2005 - 10/21/2005
Craig T. Poling Lockheed Martin 10/8/2005 - 10/10/2005
Jianliang Qian Wichita State University 10/16/2005 - 10/21/2005
Gregory J. Randall Universidad de la Republica 8/18/2005 - 7/31/2006
Fernando Reitich University of Minnesota 10/17/2005 - 10/21/2005
Jeff Remillad Ford Motor Company 10/13/2005 - 10/14/2005
Rosemary Renaut Arizona State University 10/30/2005 - 11/18/2005
Rosemary Renaut Arizona State University 9/18/2005 - 10/7/2005
Walter Richardson University of Texas - San Antonio 9/1/2005 - 6/30/2006
Partha S. Routh Boise State University 10/16/2005 - 10/21/2005
Paul E. Sacks Iowa State University 10/16/2005 - 10/20/2005
Fadil Santosa University of Minnesota 9/1/2005 - 6/30/2006
Guillermo R. Sapiro University of Minnesota 9/1/2005 - 6/30/2006
Arnd Scheel University of Minnesota 7/15/2004 - 8/31/2006
Tom L. Scofield Calvin College 9/1/2005 - 12/31/2005
Shaun Sellers Washington University - St. Louis 9/17/2005 - 10/23/2005
Fadoulourahmane Seydou University of Maryland 10/16/2005 - 10/22/2005
Shagi-Di Shih University of Wyoming 9/18/2005 - 10/22/2005
Tatiana Soleski University of Minnesota 9/1/2005 - 8/31/2007
Jakob J. Stamnes University of Bergen 10/16/2005 - 10/21/2005
Wolfang Stefan Arizona State University 10/16/2005 - 10/22/2005
Chris Stolk University of Twente 10/16/2005 - 10/23/2005
Mark Stuff General Dynamics Advanced Information Systems 10/16/2005 - 10/21/2005
Bernd Sturmfels University of California - Berkeley 10/9/2005 - 10/10/2005
Vladimir Sverak University of Minnesota 9/1/2005 - 6/30/2006
William W. Symes Rice University 10/16/2005 - 10/21/2005
Alexandru Tamasan University of Central Florida 10/16/2005 - 10/21/2005
Fons Ten Kroode Shell Research 10/16/2005 - 10/22/2005
Ahmed Tewfik University of Minnesota 10/24/2005 - 10/24/2005
Alan Thomas Clemson University 9/4/2005 - 12/17/2005
Carl Toews University of Minnesota 9/1/2005 - 8/31/2007
Philippe Tondeur University of Illinois - Urbana-Champaign 10/8/2005 - 10/10/2005
Chrysoula Tsogka University of Chicago 10/16/2005 - 10/29/2005
Gunther A. Uhlmann University of Washington 10/16/2005 - 10/21/2005
Luc Vignaud Direction des Etudes et de Synthese 10/16/2005 - 10/21/2005
Jingyue Wang Purdue University 9/1/2005 - 6/30/2006
Xiaoqiang Wang University of Minnesota 9/1/2005 - 8/31/2007
Benjamin S. White ExxonMobil 10/16/2005 - 10/21/2005
Rebecca Willett Duke University 10/17/2005 - 10/21/2005
Ruth Williams University of California - San Diego 10/7/2005 - 10/10/2005
Margaret H. Wright New York University 10/9/2005 - 10/10/2005
Frank Wuebbeling Universitat Munster 10/5/2005 - 10/19/2005
Yuan Xu University of Oregon 10/16/2005 - 10/20/2005
Mihalis Yannakakis Columbia University 10/8/2005 - 10/10/2005
Can Evren Yarman Rensselaer Polytechnic Institute 10/17/2005 - 10/21/2005
Jeong-Rock Yoon Clemson University 9/6/2005 - 12/23/2005
Ofer Zeitouni University of Minnesota 9/1/2005 - 6/30/2006
Hongkai Zhao University of California - Irvine 10/16/2005 - 10/21/2005
Legend: Postdoc or Industrial Postdoc Long-term Visitor

Participating Institutions: Air Force Research Laboratory, Carnegie Mellon University, Consiglio Nazionale delle Ricerche (CNR), Georgia Institute of Technology, Indiana University, Iowa State University, Kent State University, Lawrence Livermore National Laboratories, Los Alamos National Laboratory, Michigan State University, Mississippi State University, Northern Illinois University, Ohio State University, Pennsylvania State University, Purdue University, Rice University, Rutgers University, Sandia National Laboratories, Seoul National University (BK21), Seoul National University (SRCCS), Texas A & M University, University of Chicago, University of Cincinnati, University of Delaware, University of Houston, University of Illinois - Urbana-Champaign, University of Iowa, University of Kentucky, University of Maryland, University of Michigan, University of Minnesota, University of Notre Dame, University of Pittsburgh, University of Texas - Austin, University of Wisconsin - Madison, University of Wyoming, Wayne State University
Participating Corporations: 3M, Boeing, Corning, ExxonMobil, Ford Motor Company, General Electric, General Motors, Honeywell, IBM Corporation, Johnson & Johnson, Lockheed Martin, Medtronic, Inc., Motorola, Schlumberger-Doll Research, Siemens, Telcordia Technologies