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### November 2005

2005-2006 Program

### Imaging

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

IMA Events

### Frontiers in Imaging

#### November 7-11, 2005

Organizers: F. Alberto Grunbaum (University of California - Berkeley), Dennis M. Healy, Jr. (DARPA)

#### http://www.ima.umn.edu/imaging/W11.7-11.05/index.html

Modern technical means coupled with state of the art mathematics are promising to provide quantitative imaging information about structures and phenomena long assumed to be inaccessible to imaging. This worskhop will consider the mathematical enablers required as imaging pushes to the new frontiers including imaging the electron wave functions of atoms and molecules, mapping single electron spins in a semiconductor or macromolecule, and fathoming the spatiotemporal state of huge distributed networks such as the internet or power grids. Specific modalities to be studied include network tomography; molecular, nanoscale, and quantum state imaging, magnetic resonance force microscopy; and cryogenic x-ray tomography. We also consider the mathematical approaches to building information from the synthesis and fusion of multiple imaging modalities.
Schedule

## Tuesday, November 1

 11:15a-12:15p Numerical integration, energy and weighted approximation Steven Benjamin Damelin (University of Minnesota) Lind Hall 409 PS

## Wednesday, November 2

 11:15a-12:15p Level set method tutorial II: Numerical algorithms for Hamilton-Jacobi Equations and level set methods for image segmentation Chiu Yen Kao (University of Minnesota) Lind Hall 409

## Thursday, November 3

 11:15a-12:15p Approximation methods and stability of singular integral equations on the line: A tale of several countries Steven Benjamin Damelin (University of Minnesota) Vincent Hall 570 SMS 3:30p-4:30p Discretization versus Reconstruction: A random walk through numerical integration and low discrepancy sequences on rectifiable sets Steven Benjamin Damelin (University of Minnesota) Vincent Hall 16 PS

## Friday, November 4

 1:25p-2:25p Vital Images, Inc.: Advanced analysis of medical images in the clinical practice Marek Brejl (Vital Images, Inc.) Vincent Hall 20 IPS

## Monday, November 7

 9:00a-9:30a Registration and coffee EE/CS 3-176 W11.7-11.05 9:30a-9:45a Welcome to the IMA Douglas N. Arnold (University of Minnesota) EE/CS 3-180 W11.7-11.05 9:45a-10:30a Opening remarks F. Alberto Grunbaum (University of California - Berkeley) Dennis M. Healy, Jr. (DARPA) EE/CS 3-180 W11.7-11.05 10:30a-11:00a coffee EE/CS 3-176 W11.7-11.05 11:00a-12:00p Compressive Imaging: A New Framework for Computational Image Processing Richard Baraniuk (Rice University) EE/CS 3-180 W11.7-11.05 12:00p-2:00p lunch W11.7-11.05 2:00p-3:00p The Compressive Optical MONTAGE Photography Initiative David J. Brady (Duke University) EE/CS 3-180 W11.7-11.05 3:00p-3:30p coffee EE/CS 3-176 W11.7-11.05 3:30p-4:00p Second Chances: Questions and round table on compressive sensing EE/CS 3-180 W11.7-11.05 4:00p-4:10p Group photo W11.7-11.05 4:15p-5:30p Reception and poster session Lind Hall 400 W11.7-11.05 Image normalization by mutual information Evgeniy Bart (University of Minnesota) Fourier Domain Estimation for Network Tomography (Wednesday only) Jin Cao (Lucent Technologies) Static Multimodal Multiplex Spectrometer Design for Chemometrics of Diffuse Sources Michael E. Gehm (Duke University) Restoration and zoom of irregularly sampled, blurred and noisy images by accurate total variation minimization with local constraints Gloria Haro Ortega (University of Minnesota) Sparsity constrained imaging problems Alfred Hero (University of Michigan) Topological-Geometric Shape Model for 3D Object Representation Hamid Krim (North Carolina State University) Direct Reconstruction-Segmentation, as Motivated by Electron Microscopy Hstau Liao (University of Minnesota) Introductions: MUSIC meets Linear Sampling meets the Point Source Method Russell Luke (University of Delaware) Estimating Imaging Artifacts Caused by Leading-Order Internal Multiples Alison Malcolm (University of Minnesota) Challenges in Improving Sensitivity for Quantification of PET Data in Alzheimer's Disease Studies: Image Restoration and Registration Rosemary Renaut (Arizona State University) Some New Wavelets in Medical Imaging Tatiana Soleski (University of Minnesota) Refractive Index Based Tomography Alan Thomas (Clemson University) Clustering of hyperspectral Raman imaging data with a differential wavelet-based noise removal approach Yu-Ping Wang (University of Missouri - Kansas City) Localized Band-Limited Image Representation and Denoising Hong Xiao (University of California - Davis) Elastography: Creating elasticity images of tissue using propagating shear waves Jeong-Rock Yoon (Clemson University)

## Tuesday, November 8

 9:15a-9:30a coffee EE/CS 3-176 W11.7-11.05 9:30a-10:30a Tracking Normality in Networks Mark Coates (McGill University) EE/CS 3-180 W11.7-11.05 10:30a-11:00a coffee EE/CS 3-176 W11.7-11.05 11:00a-12:00p Drawing power law networks using a local/global decomposition Fan Chung Graham (University of California - San Diego) EE/CS 3-180 W11.7-11.05 12:00p-2:00p lunch W11.7-11.05 2:00p-3:00p Applications of femtosecond laser pulse shaping to deep tissue imaging Warren S. Warren (Duke University) EE/CS 3-180 W11.7-11.05 3:00p-3:30p coffee EE/CS 3-176 W11.7-11.05 3:30p-4:00p Second chances EE/CS 3-180 W11.7-11.05

## Wednesday, November 9

 9:15a-9:30a coffee EE/CS 3-176 W11.7-11.05 9:30a-10:30a Inversion of Autocorrelation Functions James R. Fienup (University of Rochester) EE/CS 3-180 W11.7-11.05 10:30a-11:00a coffee EE/CS 3-176 W11.7-11.05 11:00a-12:00p Emerging Techniques for Solving NP-Complete Problems in Mathematics, Biology, Engineering ... and Physics John A. Sidles (University of Washington) EE/CS 3-180 W11.7-11.05 12:00p-2:00p lunch W11.7-11.05 2:00p-3:00p Adaptive manipulation of objects in Hilbert Space via strong field lasers Robert J. Levis (Temple University) EE/CS 3-180 W11.7-11.05 3:00p-3:30p coffee EE/CS 3-176 W11.7-11.05 3:30p-4:00p Second chances EE/CS 3-180 W11.7-11.05 4:15p-5:30p Poster session—same posters as on Monday Lind Hall 400 W11.7-11.05 6:30p-8:00p Workshop Dinner (sign up by noon Tuesday) Loring Pasta Bar W11.7-11.05

## Thursday, November 10

 9:15a-9:30a coffee EE/CS 3-176 W11.7-11.05 9:30a-10:30a Imaging with Wireless Sensor Networks Robert Nowak (University of Wisconsin - Madison) EE/CS 3-180 W11.7-11.05 10:30a-11:00a coffee EE/CS 3-176 W11.7-11.05 11:00a-12:00p Multiterminal Network Tomography Laura Felicia Matusevich (Texas A & M University) EE/CS 3-180 W11.7-11.05 12:00p-2:00p lunch W11.7-11.05 2:00p-3:00p Tomography problems on graphs George Michailidis (University of Michigan) EE/CS 3-180 W11.7-11.05 3:00p-3:30p coffee EE/CS 3-176 W11.7-11.05 3:30p-4:00p Second Chances: Questions and round table discussion EE/CS 3-180 W11.7-11.05

## Friday, November 11

 8:45a-9:00a coffee EE/CS 3-176 W11.7-11.05 9:00a-10:00a Thermoacoustic Tomography - Reconstruction of Data Measured under Clinical Constraints Sarah K. Patch (University of Wisconsin - Milwaukee) EE/CS 3-180 W11.7-11.05 10:00a-10:30a coffee EE/CS 3-176 W11.7-11.05 10:30a-11:30a 3D Optics George Barbastathis (Massachusetts Institute of Technology) EE/CS 3-180 W11.7-11.05 11:30a-1:00p lunch W11.7-11.05 1:00p-2:00p Imager design using object space prior knowledge Mark A. Neifeld (University of Arizona) EE/CS 3-180 W11.7-11.05 2:00p-2:30p Second Chances: discussion of multidomain optimization in imaging systems. EE/CS 3-180 W11.7-11.05

## Monday, November 14

 11:15a-12:15p TBA Bojan Guzina (University of Minnesota) Lind Hall 409 InvPS

## Tuesday, November 15

 11:15a-12:15p Inverse Problem in Refractive Index Optical Tomography Taufiquar Khan (Clemson University) Lind Hall 409 PS

## Friday, November 18

 1:25p-2:25p The Map-seeking Method: From Cortical Theory to Inverse-Problem Method David Arathorn (General Intelligence Corporation) 113 Vincent Hall IPS

## Thursday, November 24

 All Day Thanksgiving. The IMA is closed.

## Friday, November 25

 All Day Thanksgiving recuperation. The IMA is closed.

## Monday, November 28

 11:15a-12:15p A New Level Set Method for Image Segmentation Without Reinitialization Changfeng Gui (University of Connecticut) Lind Hall 409 VIRP
Abstracts
 David Arathorn (General Intelligence Corporation) The Map-seeking Method: From Cortical Theory to Inverse-Problem Method Abstract: The Map-Seeking Method provides a tractable solution for the inverse problem of discovering a composition of transformations that map one pattern to another. It was invented (or uncovered) as part of an attempt to hypothesize how the visual cortices solve the problem of transformation discovery, with the intent of applying the same principle to machine vision. To establish a base level of biological plausibility for this mathematical approach it was shown that there are reasonably realistic neuronal circuits that implement a functional equivalent of the algorithmic form of the method. As a result, the general implementation of the method has come to be known as the Map-Seeking Circuit (MSC). Most of the research into practical application of the MSC has been directed at machine vision and image processing. However, during the last few years it has become apparent that the MSC is applicable to various classes of inverse problems partly or entirely outside of vision. Most recent focus has been on classes of problems which require concurrent solution in multiple domains or problem spaces, for which a minor variant of the original MSC provides an elegant and practical solution. These include both "brain-instinctual" tasks and "brain-taxing" problems, and a preliminary insight into the difference will be discussed. Richard Baraniuk (Rice University) Compressive Imaging: A New Framework for Computational Image Processing Abstract: Imaging sensors, hardware, and algorithms are under increasing pressure to accommodate ever larger and higher-dimensional data sets; ever faster capture, sampling, and processing rates; ever lower power consumption; communication over ever more difficult channels; and radically new sensing modalities. Fortunately, over the past few decades, there has been an enormous increase in computational power and data storage capacity, which provides a new angle to tackle these challenges. We could be on the verge of moving from a "digital signal processing" (DSP) paradigm, where analog signals (including light fields) are sampled periodically to create their digital counterparts for processing, to a "computational signal processing" (CSP) paradigm, where analog signals are converted directly to any of a number of intermediate, "condensed" representations for processing using optimization techniques. At the foundation of CSP lie new uncertainty principles that generalize Heisenberg's between the time and frequency domains and the concept of compressibility. As an example of CSP, I will overview "Compressive Imaging", an emerging field based on the revelation that a small number of linear projections of a compressible image contain enough information for image reconstruction and processing. The implications of compressive imaging are promising for many applications and enable the design of new kinds of imaging systems and cameras. For more information, a compressive imaging resource page is available on the web at dsp.rice.edu/cs George Barbastathis (Massachusetts Institute of Technology) 3D Optics Abstract: 3D optical elements modulate light through interaction with an entire volume of variable refractive index (as opposed to a sequence of surfaces used in traditional optics.) One commonly used form of 3D optics is gradient-index (GRIN) where the modulation is base-band. Instead, we have emphasized use of modulations on a spatial carrier (grating.) We have demonstrated that the resulting controllable shift variance and dispersion can be used for optical slicing, real-time optical tomography, and hyper-spectral imaging in three spatial dimensions. The extended degrees of freedom available in defining the optical response of 3D optics with a carrier makes this kind of optical elements suitable for computational imaging. We will discuss examples where over-constrained least-squares (pseudo-inverse) and maximum likelihood (Viterbi) algorithms were used to maximize the image information extracted from the raw images. Evgeniy Bart (University of Minnesota) Image normalization by mutual information Abstract: Image normalization refers to eliminating image variations (such as noise, illumination, or occlusion) that are related to conditions of image acquisition and are irrelevant to object identity. Image normalization can be used as a preprocessing stage to assist computer or human object perception. In this paper, a class-based image normalization method is proposed. Objects in this method are represented in the PCA basis, and mutual information is used to identify irrelevant principal components. These components are then discarded to obtain a normalized image which is not affected by the specific conditions of image acquisition. The method is demonstrated to produce visually pleasing results and to improve significantly the accuracy of known recognition algorithms. The use of mutual information is a significant advantage over the standard method of discarding components according to the eigenvalues, since eigenvalues correspond to variance and have no direct relation to the relevance of components to representation. An additional advantage of the proposed algorithm is that many types of image variations are handled in a unified framework. David J. Brady (Duke University) The Compressive Optical MONTAGE Photography Initiative Abstract: COMP-I is a program under the DARPA MONTAGE program focusing on the construction of thin digital imaging systems. COMP-I uses optical prefilters to encode the impulse response of multiple aperture imaging systems. The COMP-I program is near the completion of phase I development and has produced both visible and IR imaging systems based on focal plane coding and diffractive coding elements. This talk will review the design philosophy of COMP-I and describe recent experimental results. The talk will focus in particular on image inference strategies from compressively sampled measurements. Jin Cao (Lucent Technologies) Fourier Domain Estimation for Network Tomography Abstract: Network tomography has been regarded as one of the most promising methodologies for performance evaluation and diagnosis of the massive and decentralized Internet. It can be used to infer unobservable network behaviors from directly measurable metrics and does not require cooperation between network internal elements and the end users. For instance, the Internet users may estimate link level characteristics such as loss and delay from end-to-end measurements, whereas the network operators can evaluate the Internet path-level traffic intensity based on link-level traffic measurements. In this paper, we present a novel estimation approach for the network tomography problem. Unlike previous methods, we do not work with the model distribution directly, but rather we work with its characteristic function that is the Fourier transform of the distribution. In addition, we also obtain some identifiability results that apply not only to specific distribution models such as discrete distributions but also to general distributions. We focus on network delay tomography and develop a Fourier domain inference algorithm based on flexible mixture models of link delays. Through extensive model simulation and simulation using real Internet trace, we are able to demonstrate that the new algorithm is computationally more efficient and yields more accurate estimates than previous methods especially for a network with heterogeneous link delays. Mark Coates (McGill University) Tracking Normality in Networks Abstract: Many anomalous network events do not manifest themselves as abrupt, easily-detectable changes in the volume of traffic at a single switch. Rather, the footprint they leave is a modification of the pattern of traffic at a number of routers in this network. Anomaly detection is then a question of whether the current traffic pattern is sufficiently divergent from "normal" traffic patterns. In this talk, I will describe a technique for sequentially constructing a sparse kernel dictionary that forms a map of network normality and illustrate how this map can be used to identify anomalous events. Steven Benjamin Damelin (University of Minnesota) Numerical integration, energy and weighted approximations Abstract: This talk will discuss recent work of the author, P. Grabner and G. Mullen. We will first discuss the relationship between numerical integration and energy functionals on the sphere and show that points on the sphere that minimize certain energy functionals are well distributed in the sense that their error of numerical integration is small. An example of a point system which admits t-designs for some t and good energy estimates is constructed. Steven Benjamin Damelin (University of Minnesota) Approximation methods and stability of singular integral equations on the line: A tale of several countries Abstract: In the subjects of target recognition and earthquake predication, there arise classes of integral equations with Cauchy singular kernels. An important subclass of such equations, which are of present interest to geoscientists and mathematical physicists are classes where the underlying data is defined over an unbounded domain, such as the real line. Up until recently, the study of such classes of equations has been hampered due to the lack of natural tools to deal with such problems. In this paper, we show that there exist positive, finite numbers mu which allow us to approximate singular integral equations on the line of the form mu w^2 f - K[f] = g w^{2+\delta}.Here w is a fixed even exponential weight of smooth polynomial decay at plus or minus infinity, delta > 0, K[.]:=H[. w^2]/pi is a weighted Hilbert transform and g is a fixed real valued function in a weighted locally Lipschitz space of order 0 < lambda < 1. I will discuss the problem and the interesting tale which allowed us to deal with it. Tne talk will be easy to follow, both for faculty and graduate/undergraduate students. This is joint work with K. Diethelm and is supported, in part, by a EPSRC Fellowship (with the University of Leicester). Steven Benjamin Damelin (University of Minnesota) Discretization versus Reconstruction: A random walk through numerical integration and low discrepancy sequences on rectifiable sets Abstract: Distributing a large number of points uniformly on a compact set is an interesting and difficult problem which has attracted much research. In this talk we will focus on some recent work of the author and his collaborators, dealing with the interplay between numerical integration, low discrepacny sequences and reconstruction. For example, we will study certain arrangements of N geq 1 points on sets A from a class Ad of d-dimensional compact sets embedded in Rd', 1 leq d leq d'. As an example, we can take the d dimensional unit sphere Sd realized as a subset of Rd+1. We assume that these points interact through a Riesz potential V=| |-s, where s>0 and | | is the Euclidean distance in Rd'. In particular, we will focus on the following ideas and new methods developed in the case of the following items 1-3 below. Even in special cases such as the sphere, most of what we develop below was until recently not known. (1) The development of a numerical integration formula in terms of Riesz energy which allows for discrepancy estimates on spheres for a large class of smooth functions, typically Lipchitz of positive order. (2) Estimates for separation and mesh norm of s between 0 and d-1 minimal extremal configurations and associated biological scar defects. (3) The existence of low discrepancy sequences such as nets built out of bases of linear independent vectors with applications to combinatorial designs and codes. References: (See www.ima.umn.edu/~damelin). -S. B. Damelin, J. Leversley, V. Maymeskul and X. Sun, Numerical integration, Zonal kernels and Energy on compact homogenous manifolds. See: http://www.ima.umn.edu/~damelin/dlms.pdf -S. B. Damelin, Yale, October 2005: A random walk through numerical integration, Riesz configurations and low discrepancy sequences on rectifiable sets. See: http://www.ima.umn.edu/~damelin/yale05.pdf James R. Fienup (University of Rochester) Inversion of Autocorrelation Functions Abstract: Solving the phase retrieval problem, i.e. reconstructing a compact, multidimensional function from the modulus of its Fourier transform, has applications in astronomy, x-ray diffraction, optical wave-front sensing, and other areas of physics and engineering. To solve such problems, one must have constraints on the function in order to have a chance for a unique solution. For some of these problems, the most important constraint is S, the support of the function, i.e., the set of points outside of which the function has value zero. The autocorrelation of the function can computed from the Fourier modulus, and A, the support of the autocorrelation function, is the Minkowski sum of S with -S. Therefore, in order to solve the phase retrieval problem, we first want to determine S, or at least estimate the smallest upper bound on S, from A = S - S. This paper will describe methods we have discovered so far for performing this inversion with the hope that others will point us to, or discover, additional approaches. Michael E. Gehm (Duke University) Static Multimodal Multiplex Spectrometer Design for Chemometrics of Diffuse Sources Abstract: We have developed a broad class of coded aperture spectrometer designs for spectroscopy of diffuse biological and chemical sources. In contrast to traditional designs, these spectrometers do not force a tradeoff between resolution and throughput. As a result, they are ideal for precision chemometric studies of weak, diffuse sources. I will discuss the nature of the coding design and present results showing high-precision concentration estimation of metabolites at clinical levels. Fan Chung Graham (University of California - San Diego) Drawing power law networks using a local/global decomposition Abstract: It has been noted that many realistic networks have a power law degree distribution and exhibit the small world phenomenon. We consider graph drawing methods that take advantage of recent developments in the modeling of such networks. Our main approach is to partition the edge set of a graph into local'' edges and "global" edges, and to use a force-directed method that emphasizes the local edges. We show that our drawing method works well for networks that contain underlying geometric graphs augmented with random edges, and demonstrate the method on a few examples. We present fast approximation algorithms for the maximum short flow problem, and for testing whether a short flow of a certain size exists between given vertices. Using these algorithms, we give a fast approximation algorithm for determining local subgraphs of a given graph. The drawing algorithm we present can be applied to general graphs, but is particularly well-suited for numerous small-world networks with power law degree distribution. This is a joint work with Reid Andersen and Linyuan Lu. Gloria Haro Ortega (University of Minnesota) Restoration and zoom of irregularly sampled, blurred and noisy images by accurate total variation minimization with local constraints Abstract: Joint work with A. Almansa, V. Caselles and B. Rouge. We propose an algorithm to solve a problem in image restoration which considers several different aspects of it, namely: irregular sampling, denoising, deconvolution, and zooming. Our algorithm is based on an extension of a previous image denoising algorithm proposed by A. Chambolle using total variation, combined with irregular to regular sampling algorithms proposed by H.G. Feichtinger, K. Gröchenig, M. Rauth and T. Strohmer. Finally we present some experimental results and we compare them with those obtained with the algorithm proposed by K. Gröchenig et al. Alfred Hero (University of Michigan) Sparsity constrained imaging problems Abstract: Joint with Michael Ting and Raviv Raich. In many imaging problems a sparse reonstruction is desired. This could be due to natural domain of the image, e.g., in molecular imaging only a few voxels are non-zero, or a desired sparseness property, e.g., detection of corner reflectors in radar imaging. We present several new methods for sparse reconstruction that account for positivity constraints, convolution kernels, and unknown sparsity factors. For illustration we apply these methods to reconstructing magnetic force resonance microscopy images of compounds such as Benzene and DNA. Hamid Krim (North Carolina State University) Topological-Geometric Shape Model for 3D Object Representation Abstract: We propose a new method for encoding the geometry of surfaces embedded in three-dimensional space. For a compact surface representing the boundary of a three-dimensional solid, the distance function is used to construct a skeletal graph that is invariant with respect to translations, rotations, and scaling. The skeletal graph is then equipped with weights that capture the geometry of the surface. The information stored in the weighted graph is sufficient for the restoration of the original surface. This proposed approach leads to robust modeling of surfaces; independent of their scale and position in a three-dimensional space. Robert J. Levis (Temple University) Adaptive manipulation of objects in Hilbert Space via strong field lasers Abstract: We propose a new approach to classical detection problem of discrimination of a true signal from an interferent signal. We show that the detection performance, as quantified by the receiver operating curve (ROC), can be substantially improved when the signal is represented by a multi-component data set that is actively manipulated by a shaped probing pulse. In this case, the signal sought (agent) and the interfering signal (interferent) are visualized by vectors in a multi-dimensional detection space. Separation of these vectors is achieved by adaptive modification of a probing laser pulse to actively manipulate the Hamiltonian of the agent and interferent. We demonstrate one implementation of the concept of adaptive rotation of signal vectors to chemical agent detection by means of strong-field time-of-flight mass-spectrometry. Hstau Liao (University of Minnesota) Direct Reconstruction-Segmentation, as Motivated by Electron Microscopy Abstract: Quite often in electron microscopy it is desired to segment the reconstructed volumes of biological macromolecules. Knowledge of the 3D structure of the molecules can be crucial for the understanding of their biological functions. We propose approaches that directly produce a label (segmented) image from the tomograms (projections). Knowing that there are only a finitely many possible labels and by postulating a Gibbs prior on the underlying distribution of label images, we show that it is possible to recover the unknown image from only a few noisy projections. Russell Luke (University of Delaware) Introductions: MUSIC meets Linear Sampling meets the Point Source Method Abstract: Cheney and later Kirsch showed that the Factorization Method of Kirsch is equivalent to Devaney's MUSIC algorithm for the case of scattering from inhomogeneous media. We demonstrate a similar correspondence between the Linear Sampling Method of Colton and Kirsch as well as the Point Source Method of Potthast and the MUSIC Algorithm for scattering from extended perfect conductors. We extract the most attractive aspects of each algorithm for a robust and simple proceedure for determining the support of extended scatterers from far field data. Alison Malcolm (University of Minnesota) Estimating Imaging Artifacts Caused by Leading-Order Internal Multiples Abstract: Seismic imaging typically assumes that all recorded energy has scattered only once in the subsurface. To satisfy this assumption, attempts are made to attenuate waves which have scattered more than once (multiples), before the image is formed. We propose a method of estimating the image artifacts caused by leading-order internal multiples directly in the image to reduce the difficulties caused by inaccurately estimating the multiples. Laura Felicia Matusevich (Texas A & M University) Multiterminal Network Tomography Abstract: We consider a very general inverse problem on directed graphs. Surprisingly, this problem can actually be solved, explicitly, in a large class of examples. I will describe the construction of these examples, as well as the method used to produce the inversion formulas. This is joint work with F. Alberto Grunbaum. George Michailidis (University of Michigan) Tomography problems on graphs Abstract: In this talk we examine a class of inverse problems that arise on graphs. We provide a review of recent developments, including design aspects for identifiability purposes, inference issues and applications to computer networks. Mark A. Neifeld (University of Arizona) Imager design using object space prior knowledge Abstract: Traditional optical design typically exploits only limited prior knowledge of the object space to be imaged (e.g., resolution, field of view, nominal range, etc.) It is possible to include stronger object space constraints (e.g., specific objects of interest, operational SNR, background characteristics, etc.) into the optical design and thus generate a more photo-efficient solution. In this talk I will discuss both passive and active feature-specific imaging systems for this purpose. Sarah K. Patch (University of Wisconsin - Milwaukee) Thermoacoustic Tomography - Reconstruction of Data Measured under Clinical Constraints Abstract: pdf Rosemary Renaut (Arizona State University) Challenges in Improving Sensitivity for Quantification of PET Data in Alzheimer's Disease Studies: Image Restoration and Registration Abstract: With the increase in life expectancy of the general population, the incidence of Alzheimer's Diease is growing rapidly and impacts the lives of those with the disease and their care givers, as well as the entire medical infrastructure. Research associated with AD focuses on early diagnosis, and effective treatment and prevention strategies using neuroimaging biomarkers which have demonstrated high sensitivity and specificity. Many studies use PET data to measure differences in cerebral metabolic rates for glucose before onset of the disease in the carriers of APOE \$\epsilon 4\$. Researchers hope to rapidly evaluate various preventive strategies on healthy subjects which requires refining and extending technologies for reliable detection of small scale features indicating functional or structural change. Appropriate computational techniques must be developed and validated. The PET working group of the National Institute of Aging recently published recommendations for studies on aging that utilize imaging data, acknowledging prior limitations of PET studies, while providing guidelines and protocols for future neuroimaging research. We present initial results of restoration and registration techniques for quantifying functional PET images. John A. Sidles (University of Washington) Emerging Techniques for Solving NP-Complete Problems in Mathematics, Biology, Engineering ... and Physics Abstract: Complex systems are ubiquitous in mathematics, biology, engineering, and physics, and the past ten years have witnessed an exponential increase in the literature associated such systems. A shared conceptual framework is becoming apparent among challenges as seemingly different as the following: the search by mathematicians for exact high-order trigonometric identities, the search by engineers for stable control systems, the search by biologists for stable protein structures, and the search by condensed matter physicists for ground states. Recent work has shown that separated product-sum representations provide a powerful and broadly applicable tool for analyzing complex systems. Beylkin and Mohlenkamp provide a good introduction to these representations in their recent preprint "Algorithms for Numerical Analysis in High Dimensions" (*). This talk will review some of the basic ideas of separated product-sum representations, and discuss how our UW Quantum System Engineering (QSE) Group is applying these ideas in polynomial-time simulations of large-scale quantum spin systems. Our QSE Group has found that Beylkin and Mohlenkamp's methods can be readily extended to dynamical systems by a two-fold trick: (1) introduce noise, and (2) convert the noise to an equivalent measurement processes. The second step exploits the same unitary invariance of operator-sum representations that plays a central role in quantum computing theory. The resulting quantum trajectories are readily projected onto low- dimensional manifolds of Beylkin-Mohlenkamp type, where they can be integrated using polynomial-time numerical algorithms. The practical consequence is that a broad class of problems in quantum physics and engineering that were previously thought to be in the (intractable) complexity class EXP can now be solved by algorithms that are in the (much simpler) complexity class NP. The lecture will close with an informal survey of physics problems that might be addressed by these methods. (*) http://amath.colorado.edu/activities/preprints/archive/519.pdf Tatiana Soleski (University of Minnesota) Some New Wavelets in Medical Imaging Abstract: Joint work with Gilbert Walter. In Computerized Tomography (CT) an image must be recovered from data given by the Radon transform of the image. This data is usually in the form of sampled values of the transform. In our work a method of recovering the image is based on the sampling properties of the prolate spheroidal wavelets which are superior to other wavelets. It avoids integration and allows the precomputation of certain coefficients. The approximation based on this method is shown to converge to the true image under mild hypotheses. Another interesting application of wavelets is in functional Magnetic Resonance Imaging (fMRI). To estimate the total intensity of the image over the region of interest, a new method based on multi-dimensional prolate spheroidal wave functions (PSWFs) was proposed in a series of papers beginning with the work of Shepp and Zhang. We try to determine how good the proposed approximations are and how they can be improved. Alan Thomas (Clemson University) Refractive Index Based Tomography Abstract: In optical tomography, conventionally the diffusion approximation to the radiative transport equation (RTE) with a constant refractive index is used to image highly scattering or turbid media. Recently we derived the relevant RTE and its spherical harmonics approximation with a spatially varying refractive index. We found that the model with spatially varying refractive index for photon transport is substantially different than the spatially constant model. We formulate the optical tomography inverse problem based on the diffusion approximation to image a highly scattering medium with a spatially varying refractive index. We have simulated the forward and the inverse problem using the finite element method and have reconstructed the spatially varying refractive index parameter in our model for the inverse problem. Our simulations indicate that the refractive index based optical tomography shows promise for the reconstruction of the refractive index parameter. Yu-Ping Wang (University of Missouri - Kansas City) Clustering of hyperspectral Raman imaging data with a differential wavelet-based noise removal approach Abstract: Raman spectral imaging has been widely used for extracting chemical information from biological specimens. One of the challenging problems is to cluster the chemical groups from the vast amount of hyperdimensional spectral imaging data so that functionally similar groups can be identified. Furthermore, the poor signal to noise ratio makes the problem more difficult. In this work, we introduce a novel approach that combines a differential wavelet based noise removal approach with a fuzzy clustering algorithm for the pixel-wise classification of Raman image. The preprocessing of the spectral data is facilitated by decomposing them in a special family of differential wavelet domain, where the discrimination of true spectral features and noises can be easily performed using a multi-scale pointwise product criterion. The performance of the proposed approach is evaluated by the improvement over the subsequent clustering of a dentin/adhesive interface specimen under different noise levels. In comparison with conventional denoising algorithms, the proposed approach demonstrates the super performance. This is a joint work with Wang Yong and Paulette Spencer of the School of Dentistry at the University of Missouri-Kansas City. Hong Xiao (University of California - Davis) Localized Band-Limited Image Representation and Denoising Abstract: A mathematical framework based on band-limited functions has been developed for modeling and analyzing images in two dimensions. The foundation of this framework is a class of basis functions that are locally compact in both frequency and image domains. Images represented in such bases are visually smooth with neither ringing nor blocky artifacts which frequently company processed images, and at the same time preserve the original sharpness. Preliminary results in image denoising will be presented. Jeong-Rock Yoon (Clemson University) Elastography: Creating elasticity images of tissue using propagating shear waves Abstract: Elastography is an innovative new medical imaging technique that provides high resolution/contrast images of elastic stiffness identifying abnormalities not seen by standard ultrasound. Since the elastic stiffness increases signicantly (up to 10 times) in cancerous tissue, elastography shows tumor as a bright spot in the reconstructed image. Our data is the time dependent (10,000 frames/sec) interior displacements (0.3mm grid spacing) initiated by a short-time pulse. While standard inverse problems utilizing only boundary data suffer from the inherent ill-posedness, our inverse problem for elastography doesn't because it utilizes interior information. For the isotropic tissue model, a series of uniqueness results for our inverse problem are presented, and a fast stable algorithm to reconstruct the shear stiffness based on arrival time is explained. For the anisotropic tissue model, we assume an incompressible transversely isotropic model. It is important to consider anisotropic tissue models, since some tumors exhibit anisotropy and the structure of fiber orientation has a strong correlation with the malignancy of tumor. In this model, two shear stiffness and the fiber orientation are recon- structed by four measurements of SH-polarized shear waves, which are initiated by line sources in the interior of human body based on supersonic remote pal- pation interior excitation.
Visitors in Residence
 Jung-Ha An University of Minnesota 9/1/2005 - 8/31/2007 Fredrik Andersson Lund University 9/16/2005 - 11/14/2005 David Arathorn General Intelligence Corporation 11/17/2005 - 11/19/2005 Douglas N. Arnold University of Minnesota 7/15/2001 - 8/31/2006 Donald G. Aronson University of Minnesota 9/1/2002 - 8/31/2006 Richard Baraniuk Rice University 11/6/2005 - 11/10/2005 George Barbastathis Massachusetts Institute of Technology 11/6/2005 - 11/11/2005 Evgeniy Bart University of Minnesota 9/1/2005 - 8/31/2007 Francisco Blanco-Silva Purdue University 9/1/2005 - 6/30/2006 Brett Borden Naval Postgraduate School 10/1/2005 - 12/31/2005 David J. Brady Duke University 9/18/2005 - 12/10/2005 Dennis Braunreiter SAIC 11/6/2005 - 11/11/2005 Marek Brejl Vital Images, Inc. 11/4/2005 - 11/4/2005 Robert Burridge Massachusetts Institute of Technology 9/1/2005 - 12/31/2005 Jin Cao Lucent Technologies 11/7/2005 - 11/10/2005 Qianyong Chen University of Minnesota 9/1/2004 - 8/31/2006 Margaret Cheney Rensselaer Polytechnic Institute 9/6/2005 - 12/31/2005 Hyeong In Choi Seoul National University 11/6/2005 - 11/11/2005 Edwin K. P. Chong Colorado State University 11/15/2005 - 11/17/2005 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 Mark Coates McGill University 11/6/2005 - 11/11/2005 Douglas Cochran Arizona State University 11/6/2005 - 11/11/2005 Adela Comanici Isaac Newton Institute for Mathematical Sciences 11/5/2005 - 11/11/2005 Steven Benjamin Damelin University of Minnesota 8/9/2005 - 6/30/2006 Anthony J. Devaney Northeastern University 9/5/2005 - 12/30/2005 Brian DiDonna University of Minnesota 9/1/2004 - 8/31/2006 Minh N. Do University of Illinois - Urbana-Champaign 11/7/2005 - 11/11/2005 Fariba Fahroo AFOSR/NM 11/6/2005 - 11/9/2005 Yi Fang Rensselaer Polytechnic Institute 9/12/2005 - 12/20/2005 James R. Fienup University of Rochester 11/6/2005 - 11/11/2005 Michael E. Gehm Duke University 11/6/2005 - 11/11/2005 Anne Gelb Arizona State University 11/28/2005 - 12/16/2005 Fan Chung Graham University of California - San Diego 11/6/2005 - 11/11/2005 F. Alberto Grunbaum University of California - Berkeley 11/6/2005 - 11/11/2005 Changfeng Gui University of Connecticut 9/12/2005 - 6/30/2006 Bojan Guzina University of Minnesota 11/14/2005 - 11/14/2005 Jooyoung Hahn KAIST 8/26/2005 - 7/31/2006 Gloria Haro Ortega University of Minnesota 9/1/2005 - 8/31/2007 Dennis M. Healy, Jr. DARPA 11/6/2005 - 11/11/2005 Alfred Hero University of Michigan 11/7/2005 - 11/9/2005 Michael Hofer Vienna University of Technology 11/7/2005 - 11/11/2005 Xiang Huang University of Connecticut 9/1/2005 - 6/30/2006 Xiaoming Huo Georgia Institute of Technology 11/6/2005 - 11/11/2005 Sookyung Joo University of Minnesota 9/1/2004 - 8/31/2006 Chiu Yen Kao University of Minnesota 9/1/2004 - 8/31/2006 Taufiquar Khan Clemson University 9/4/2005 - 12/31/2005 Hamid Krim North Carolina State University 11/7/2005 - 11/11/2005 Matthias Kurzke University of Minnesota 9/1/2004 - 8/31/2006 Song-Hwa Kwon University of Minnesota 8/30/2005 - 8/31/2007 Chang-Ock Lee KAIST 8/1/2005 - 7/31/2006 Jim Leger University of Minnesota 11/7/2005 - 11/11/2005 Robert J. Levis Temple University 11/6/2005 - 11/11/2005 Debra Lewis University of Minnesota 7/15/2004 - 8/31/2006 Gang Liang University of California - Irvine 11/6/2005 - 11/11/2005 Hstau Liao University of Minnesota 9/2/2005 - 8/31/2007 Brad Lucier Purdue University 8/15/2005 - 6/30/2006 Russell Luke University of Delaware 9/6/2005 - 12/31/2005 Alison Malcolm University of Minnesota 9/1/2005 - 8/31/2006 Laura Felicia Matusevich Texas A & M University 11/6/2005 - 11/12/2005 Kai Medville University of Minnesota 9/1/2005 - 8/31/2007 George Michailidis University of Michigan 11/6/2005 - 11/11/2005 Steen Moeller University of Minnesota 11/7/2005 - 11/11/2005 Jose M. F. Moura Carnegie Mellon University 11/6/2005 - 11/11/2005 Mark A. Neifeld University of Arizona 11/6/2005 - 11/11/2005 Robert Nowak University of Wisconsin - Madison 11/9/2005 - 11/10/2005 Peter J. Olver University of Minnesota 9/1/2005 - 6/30/2006 Winston Ou University of Minnesota 9/1/2005 - 1/13/2006 Victor Palamodov Tel Aviv University 10/11/2005 - 11/30/2005 Sarah K. Patch University of Wisconsin - Milwaukee 10/16/2005 - 11/12/2005 Peter Philip University of Minnesota 8/22/2004 - 8/31/2006 Nikos P. Pitsianis Duke University 11/6/2005 - 11/11/2005 Gregory J. Randall Universidad de la Republica 8/18/2005 - 7/31/2006 Rosemary Renaut Arizona State University 10/30/2005 - 11/18/2005 Walter Richardson University of Texas - San Antonio 9/1/2005 - 6/30/2006 Dmitri Romanov Temple University 11/6/2005 - 11/11/2005 Anwar Saleh University of Bahrain 11/2/2005 - 11/11/2005 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 Timothy Schulz Michigan Technological University 11/6/2005 - 11/11/2005 Tom L. Scofield Calvin College 9/1/2005 - 12/31/2005 Shagi-Di Shih University of Wyoming 11/6/2005 - 11/12/2005 John A. Sidles University of Washington 11/6/2005 - 11/9/2005 Tatiana Soleski University of Minnesota 9/1/2005 - 8/31/2007 Eddy A. Stappaerts Lawrence Livermore National Laboratories 11/6/2005 - 11/11/2005 Xiaobai Sun Duke University 11/6/2005 - 11/11/2005 Vladimir Sverak University of Minnesota 9/1/2005 - 6/30/2006 Jared Wade Tanner Stanford University 11/6/2005 - 11/11/2005 Ahmed Tewfik University of Minnesota 11/28/2005 - 11/28/2005 Alan Thomas Clemson University 9/4/2005 - 12/17/2005 Carl Toews University of Minnesota 9/1/2005 - 8/31/2007 Jingyue Wang Purdue University 9/1/2005 - 6/30/2006 Xiaoqiang Wang University of Minnesota 9/1/2005 - 8/31/2007 Yu-Ping Wang University of Missouri - Kansas City 11/6/2005 - 11/11/2005 Warren S. Warren Duke University 11/5/2005 - 11/10/2005 Rebecca Willett Duke University 11/6/2005 - 11/11/2005 Hong Xiao University of California - Davis 11/6/2005 - 11/12/2005 Jinjun Xu University of California - Los Angeles 11/6/2005 - 11/11/2005 Boli Yarkulov Novosibirsk State University of Russian Federation 11/6/2005 - 11/12/2005 Can Evren Yarman Rensselaer Polytechnic Institute 11/6/2005 - 11/11/2005 Jeong-Rock Yoon Clemson University 9/6/2005 - 12/23/2005 Ofer Zeitouni University of Minnesota 9/1/2005 - 6/30/2006 Meijun Zhu University of Oklahoma 11/6/2005 - 11/10/2005
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, Exxon Mobil, Ford Motor Company, General Electric, General Motors, Honeywell, IBM Corporation, Johnson & Johnson, Lockheed Martin, Medtronic, Inc., Motorola, Schlumberger-Doll Research, Siemens, Telcordia Technologies