Web: http://www.ima.umn.edu | Email: ima-staff@ima.umn.edu | Telephone: (612) 624-6066 | Fax: (612) 626-7370
Additional newsletters available at http://www.ima.umn.edu/newsletters

IMA Newsletter #351

January 2006

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

IMA Annual Program Year Workshop

New Mathematics and Algorithms for 3-D Image Analysis

January 9-12, 2006

Organizers: Les G. Butler (Louisiana State University), Gestur Olafsson (Louisiana State University), Eric Todd Quinto (Tufts University)

http://www.ima.umn.edu/imaging/W1.9-12.06/index.html

New mathematics and algorithms are needed for 3-D image acquisition and analysis. The 3-D images come from many disciplines: biomedicine, geology, chemistry, and microfabrication. The mathematics is wide-ranging and includes at least tomography and inverse problems, wavelets, PDE, and conformal mapping. The depth of the problem and the extent of the mathematics argue for developing long-term collaborations between mathematicians and scientists. This workshops is a step toward that end.

This workshop will focus on two topics:

A goal in the first area is to use multiple reconstructions of the raw data to better perform image segmentation. For example, edge images (e.g., using Λ-tomography) can be combined with composition images to derive a set of final images of much greater value to the experimentalists.

The analysis of simple geometric shapes has received little attention and yet could illuminate entirely new strategies in 3-D image analysis. Many non-medical problems involve high-quality images of objects with simple shapes, and this is an excellent starting point for new mathematics and algorithms.

Schedule

Monday, January 9

8:15a-8:45aRegistration and coffeeEE/CS 3-176 W1.9-12.06
8:45a-9:00aWelcome and introductionDouglas N. Arnold (University of Minnesota)EE/CS 3-180 W1.9-12.06
9:00a-9:30a3D Image Acquisition and Image Analysis AlgorithmsLes G. Butler (Louisiana State University)EE/CS 3-180 W1.9-12.06
9:30a-10:30aAn introduction to the mathematics of tomographyEric Todd Quinto (Tufts University)EE/CS 3-180 W1.9-12.06
10:30a-11:00acoffee breakEE/CS 3-176 W1.9-12.06
11:00a-12:00pRecovery of the internal grain structure of polycrystals from X-ray diffaction data using discrete tomographyGabor T. Herman (City University of New York)EE/CS 3-180 W1.9-12.06
12:00p-2:30plunch W1.9-12.06
2:30p-3:00pTBAEmmanuel J. Candes (California Institute of Technology)EE/CS 3-180 W1.9-12.06
3:00p-3:30pcoffee breakEE/CS 3-176 W1.9-12.06
3:30p-4:00pDiffraction tomography using intensity measurementsMark A. Anastasio (Illinois Institute of Technology)EE/CS 3-180 W1.9-12.06
4:00p-4:40pSecond ChancesEE/CS 3-180 W1.9-12.06
4:40p-4:45pGroup photo W1.9-12.06
4:45p-6:00pPoster Session/ReceptionLind Hall 400 W1.9-12.06
Image Reconstruction in Thermoacoustic TomographyGaik Ambartsoumian (Texas A & M University)
Peter Kuchment (Texas A & M University)
Image Segmentation using a Modified Mumford-Shah ModelJung-Ha An (University of Minnesota)
3D Image Acquisition and Image Analysis Algorithms Heath Barnett (Louisiana State University)
Les G. Butler (Louisiana State University)
Kyunmgin Ham (Louisiana State University)
Synchrotron micro computed tomography as a tool for the quantitative characterization of the structural changes during the ageing of metallic foamsOliver Brunke (University of Bremen)
Multiframe Dim Target Detection Using 3D Multiscale Geometric AnalysisBoris Aharon Efros (Ben-Gurion University of the Negev)
Frame Isotropic Multiresolution Analysis for Micro CT Scans of Coronary ArteriesAlex Gittens (University of Houston)
Factorization method in inverse obstacle scatteringNatalia Grinberg (Universitat Karlsruhe)
3D Shape Recognition and Reconstruction with Line Element GeometryMichael Hofer (Vienna University of Technology)
Segmentation and Geometry of 3D Scenes form Unorganized Point CloudsGeorge Kamberov (Stevens Institute of Technology)
Measuring features in volumetric data sets using Blob3DRichard Ketcham (University of Texas - Austin)
Zoomable PDEsSeongjai Kim (Mississippi State University)
Active Contours with Local Binary Fitting EnergyChunming Li (Vanderbilt University Institute of Imaging Science)
Method of Background Subtraction for Medical Image SegmentationHyeona Lim (Mississippi State University)
TBAW. Brent Lindquist (State University of New York - Stony Brook)
An Active Regions approach for the segmentation of 3D biological tissueGregory J. Randall (Universidad de la Republica)
Sobolev gradients and negative norms for image decompositionWalter Richardson (University of Texas - San Antonio)
Total variation imaging followed by spectral decomposition using continuous wavelet transformPartha S. Routh (Boise State University)
Structure-Preserving Filtering of DT-MRI Data: PDE and Discrete ApproachesMartin Welk (University of the Saarland)
Common reflection angle imagingGraham A. Winbow (ExxonMobil)
Sinogram decomposition for fan beam transform and its applicationsAlex Zamyatin (Bio-Imaging Research)

Tuesday, January 10

8:45a-9:00aCoffeeEE/CS 3-176 W1.9-12.06
9:00a-9:45aDual-Modality Micro-CT with Poly-Capillary X-ray OpticsErik L. Ritman (Mayo Clinic)EE/CS 3-180 W1.9-12.06
9:45a-10:30aGrain maps and grain dynamics — a reconstruction challengeHenning F. Poulsen (Riso National Laboratory)EE/CS 3-180 W1.9-12.06
10:30a-11:00acoffee breakEE/CS 3-176 W1.9-12.06
11:00a-11:45aOn mathematics of thermoacoustic imagingPeter Kuchment (Texas A & M University)EE/CS 3-180 W1.9-12.06
12:00p-2:30plunch W1.9-12.06
2:30p-3:00pImaging Translational Water Diffusion with Magnetic Resonance for Fiber Mapping in the Central Nervous SystemThomas H. Mareci (University of Florida)EE/CS 3-180 W1.9-12.06
3:00p-3:30pcoffee breakEE/CS 3-176 W1.9-12.06
3:30p-4:30pBreakout groupsEE/CS 3-180 W1.9-12.06
surface detection
segmentationW. Brent Lindquist (State University of New York - Stony Brook)
local tomographyEric Todd Quinto (Tufts University)
4:30p-5:00pSecond ChancesEE/CS 3-180 W1.9-12.06

Wednesday, January 11

8:45a-9:00aCoffeeEE/CS 3-176 W1.9-12.06
9:00a-9:45aThermoacoustic Tomography - Reconstruction of Data Measured under Clinical ConstraintsSarah K. Patch (University of Wisconsin - Milwaukee)EE/CS 3-176 W1.9-12.06
9:45a-10:30aTomography and Sampling TheoryAdel Faridani (Oregon State University)EE/CS 3-180 W1.9-12.06
10:30a-11:00acoffee breakEE/CS 3-176 W1.9-12.06
11:00a-12:00pBreakout groupsEE/CS 3-180 W1.9-12.06
samplingAdel Faridani (Oregon State University)
discrete tomographyGabor T. Herman (City University of New York)
line or path detectionThomas H. Mareci (University of Florida)
de-noisingPeter R. Massopust ( Tuboscope Pipeline Services)
exact countingHenning F. Poulsen (Riso National Laboratory)
12:00p-2:30plunch W1.9-12.06
2:30p-3:00p3D Shape-based Image Reconstruction in Diffuse Optical TomographyMisha Kilmer (Tufts University)EE/CS 3-180 W1.9-12.06
3:00p-3:30pcoffee breakEE/CS 3-176 W1.9-12.06
3:30p-4:00p3D segmentation in tomographyGuillermo R. Sapiro (University of Minnesota)EE/CS 3-180 W1.9-12.06
4:00p-4:30pProcessing of Diffusion-Tensor Magnetic Resonance ImagesAkram Aldroubi (Vanderbilt University)EE/CS 3-180 W1.9-12.06
4:30p-5:00pSecond ChancesEE/CS 3-180 W1.9-12.06
6:30p-8:00pWorkshop Dinner Gardens of Solonika W1.9-12.06

Thursday, January 12

8:45a-9:00aCoffeeEE/CS 3-176 W1.9-12.06
9:00a-9:45aElectron tomography. A short overview of methods and challengesOzan Oktem (Sidec Technologies AB)EE/CS 3-180 W1.9-12.06
9:45a-10:30aImproved cone beam local tomographyAlexander Katsevich (University of Central Florida)EE/CS 3-180 W1.9-12.06
10:30a-11:00acoffee breakEE/CS 3-176 W1.9-12.06
11:00a-12:00pBreakout groupsEE/CS 3-180 W1.9-12.06
surface detection
segmentationW. Brent Lindquist (State University of New York - Stony Brook)
line or path detectionThomas H. Mareci (University of Florida)
exact countingHenning F. Poulsen (Riso National Laboratory)
12:00p-2:30plunch W1.9-12.06
2:30p-3:15pTBAArt Wetzel (Pittsburgh Supercomputing Center)EE/CS 3-180 W1.9-12.06
3:15p-3:30pcoffee breakEE/CS 3-176 W1.9-12.06
3:30p-4:00pSummary session: What was accomplished? What's next?Les G. Butler (Louisiana State University)
Eric Todd Quinto (Tufts University)
EE/CS 3-180 W1.9-12.06

Friday, January 20

11:15a-12:15pTBA: Afra ZomorodianLind Hall 409
Abstracts
Akram Aldroubi (Vanderbilt University) Processing of Diffusion-Tensor Magnetic Resonance Images
Abstract: Diffusion-Tensor Magnetic Resonance Imaging (DT-MRI) is a relatively recent imaging modality. DT-MRI images are measurements of the diffusion tensor of water in each voxel of an imaging volume. They can be viewed as noisy, discrete, voxel-averaged samples of a continuous function from 3D space into the positive definite symmetric matrices. These DT-MRI images can be used to probe the structural and architectural features of fiber tissue such white matter and the heart ventricles. We will present an overview of the problems, methods and applications associated with DT-MRI data and their processing.
Gaik Ambartsoumian (Texas A & M University), Peter Kuchment (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 hybrid imaging technique, where the input and output signals have different physical nature. In TAT, a microwave or radiofrequency electromagnetic pulse is sent through the biological object triggering an acoustic wave measured in the exterior of the object. The resulting data is then used to recover the 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 and incomplete data problems.
Jung-Ha An (University of Minnesota) Image Segmentation using a Modified Mumford-Shah Model
Abstract: The purpose of this paper is to acquire image segmentation using a modified Mumford-Shah model. A variational region intensity based image segmentation model is proposed. The boundary of the given image is extracted by using a modified Mumford-Shah segmentation model. The proposed model is tested against synthetic data and simulated normal noisy human-brain MRI images. The experimental results provide preliminary evidence of the effectiveness of the presented model.
Mark A. Anastasio (Illinois Institute of Technology) Diffraction tomography using intensity measurements
Abstract: Diffraction tomography (DT) is a well-established imaging method for determination of the complex-valued refractive index distribution of a weakly scattering object. The success of DT imaging in optical applications, however, has been limited because it requires explicit knowledge of the phase of the measured wavefields. To circumvent the phase-retrieval problem, a theory of intensity DT (I-DT) has been proposed that replaces explicit phase measurements on a single detector plane by intensity measurements on two or more different parallel planes. In this work, we propose novel I-DT reconstruction theories that are applicable to non-conventional scanning geometries. Such advancements can improve the effectiveness of existing imaging systems and, perhaps more importantly, prompt and facilitate the development of systems for novel applications. Numerical simulations are conducted to demonstrate and validate the proposed tomographic reconstruction algorithms.
Heath Barnett (Louisiana State University), Les G. Butler (Louisiana State University), Kyunmgin Ham (Louisiana State University) 3D Image Acquisition and Image Analysis Algorithms
Abstract: Given a near-perfect X-ray source, such as a synchrotron, then what are the reasonable options for image reconstruction? Back-projection reconstruction has dominated, with lambda tomography not receiving the attention it deserves. Give the computation power at the beamline, is it reasonable to perform both reconstructions so as to discern object domains and interfaces? Second, all imaging methods reach a similar bottleneck, image analysis. Here, analysis means counting domains, identifying structure, following paths. If only the “yellow book” (Numerical Recipes: the art of scientific computing by Press, Flannery, Teukolsky, and Vettering) had another couple of chapters on algorithms for image analysis. Today, we start writing those chapters. We present some sample data sets from our work at the LSU synchrotron, the Advanced Photon Source, and the National Synchrotron Light Source. Also, we discuss potential future issues for neutron tomography at the Spallation Neutron Source.
Oliver Brunke (University of Bremen) Synchrotron micro computed tomography as a tool for the quantitative characterization of the structural changes during the ageing of metallic foams
Abstract: Metallic foams are a rather new class of porous and lightweight materials offering a unique combination of mechanical, thermal and acoustical properties. Their high stiffness to weight ratio, acoustic damping properties and thermal resistance provide possible applications in automobile industry for instance as crash energy absorbers or acoustic dampers, or in aerospace industry for lightweight parts in rockets or aircrafts. We will demonstrate methods which we use for the analysis of 3D datasets of Aluminum foams obtained at the synchrotron µCT facility at the HASYLAB/DESY. It will be shown that by means of standard 3D image processing techniques it is possible to study and quantify how different processing parameters like foaming temperature, time influence the structure formation and development of metallic foams.
Les G. Butler (Louisiana State University) 3D Image Acquisition and Image Analysis Algorithms
Abstract: Given a near-perfect X-ray source, such as a synchrotron, then what are the reasonable options for image reconstruction? Back-projection reconstruction has dominated, with lambda tomography not receiving the attention it deserves. Give the computation power at the beamline, is it reasonable to perform both reconstructions so as to discern object domains and interfaces? Second, all imaging methods reach a similar bottleneck, image analysis. Here, analysis means counting domains, identifying structure, following paths. If only the "yellow book" (Numerical Recipes: the art of scientific computing by Press, Flannery, Teukolsky, and Vettering) had another couple of chapters on algorithms for image analysis. Today, we start writing those chapters.
Boris Aharon Efros (Ben-Gurion University of the Negev) Multiframe Dim Target Detection Using 3D Multiscale Geometric Analysis
Abstract: Joint work with Dr. Ofer Levi, Industrial Engineering Department and Prof. Stanley Rotman Electrical Engineering Department, Ben-Gurion Un iversity of the Negev. We present new multi-scale geometric tools for both analysis and synthesis of 3-D data which may be scattered or observed in voxel arrays, which are typically very noisy, and which may contain one-dimensional structures such as line segments and filaments. These tools mainly rely on the 3-D Beamlet Transform (developed by Donoho et al.) offering the collection of line integrals along a strat egic multi-scale set of line segments, the Beamlet set (running through the image at different orientations, positions and lengths). 3D Beamlets methods can be applied in a wide variety of application fields that involve 3D imaging, in this work we focus on applying Bea mlet methods for the problem of dim target multi-frame detection and develop specialized tools for this application. We use tools from Gra ph theory and apply them to the special graph generated by the beamlets set.
Adel Faridani (Oregon State University) Tomography and Sampling Theory
Abstract: Computed tomography entails the reconstruction of a function from measurements of its line integrals. In this talk we explore the question: How many and which line integrals should be measured in order to achieve a desired resolution in the reconstructed image? Answering this question may help to reduce the amount of measurements and thereby the radiation dose, or to obtain a better image from the data one already has. Our exploration leads us to a mathematically and practically fruitful interaction of Shannon sampling theory and tomography. For example, sampling theory helps to identify efficient data acquisition schemes, provides a qualitative understanding of certain artifacts in tomographic images, and facilitates the error analysis of some reconstruction algorithms. On the other hand, applications in tomography have stimulated new research in sampling theory, e.g., on nonuniform sampling theorems and estimates for the aliasing error. Our dual aim is an exposition of the main principles involved as well as the presentation of some new insights.
Alex Gittens (University of Houston) Frame Isotropic Multiresolution Analysis for Micro CT Scans of Coronary Arteries
Abstract: Joint with Bernhard G. Bodmann, Donald J. Kouri, and Manos Papadakis. Recent studies have shown that as much as 85% of heart attacks are caused by the rupture of lesions comprising fatty deposits capped by a thin layer of fibrous tissue-- so-called vulnerable plaques. An imaging modality for the reliable and early detection of vulnerable plaques is therefore of significant clinical relevance. As a move in that direction, we develop a texture-based algorithm for labeling tissues in high resolution CT volume scans based upon variations in the local statistics of the wavelet coefficients. We use a fast wavelet transform associated with isotropic, three-dimensional wavelets; as a result, the algorithm is able to process large volume sets in their entirety, as opposed to two-dimensional cross-sections, and retains an orientation independent sensitivity to features at all levels. The algorithm has been applied to the classification of tissues in scans of coronary artery specimens taken using a General Electric RS-9 Micro CT scanner with a linear resolution of 27 micrometers. In the current revision, it has shown promise for reliably distinguishing fibromuscular, lipid, and calcified tissues.
Natalia Grinberg (Universitat Karlsruhe) Factorization method in inverse obstacle scattering
Abstract: Many inverse problems from acoustics, elasticity or electromagnetism can be reduced to the inverse scattering problem for the Helmholtz equation. We consider scattering by inclusions or obstacles in an homogeneous background medium. The factorization method establishes explicite relation between the spectral properties of the far field operator or its derivatives and the shape of the scatterer. This relation allows to reconstruct unknown scattering object pointwise. The factorization method works pretty well for any type of boundary condition and is dimension independent.
Gabor T. Herman (City University of New York) Recovery of the internal grain structure of polycrystals from X-ray diffaction data using discrete tomography
Abstract: Many materials (such as metals) are polycrystals: they consist of crystaline grains at various orientations. The interaction of these grains with X-rays can be detected as diffraction spots. Discrete tomography can be used to recover the internal oriention arrangement of the grains form such diffraction measurements.
Michael Hofer (Vienna University of Technology) 3D Shape Recognition and Reconstruction with Line Element Geometry
Abstract: This poster presents a new method for the recognition and reconstruction of simple geometric shapes from 3D data. Line element geometry, which generalizes both line geometry and the Laguerre geometry of oriented planes, enables us to recognize a wide class of surfaces (spiral surfaces, cones, helical surfaces, rotational surfaces, cylinders, etc.) by fitting linear subspaces in an appropriate seven-dimensional image space. In combination with standard techniques such as PCA and RANSAC, line element geometry is employed to effectively perform the segmentation of complex objects according to surface type.
George Kamberov (Stevens Institute of Technology) Segmentation and Geometry of 3D Scenes form Unorganized Point Clouds
Abstract: We present a framework to segment 3D point clouds into 0D,1D and 2D connected components (isolated points, curves, and surfaces) and then to assign robust estimates of the Gauss and mean curvatures and the principal curvature directions at each surface point. The framework is point-based. It does not use surface reconstruction, works on noisy data, no-human-in-the-loop is required to deal with non-uniformly sampled clouds and boundary points. The topology and geometry recovery are parallelizable with low overhead.
Alexander Katsevich (University of Central Florida) Improved cone beam local tomography
Abstract: A new local tomography function g is proposed. It is shown that g still contains non-local artifacts, but their level is an order of magnitude smaller than those of the previously known local tomography function. We also investigate local tomography reconstruction in the dynamic case, i.e. when the object f being scanned is undergoing some changes during the scan. Properties of g are studied, the notion of visible singularities is suitably generalized, and a relationship between the wave fronts of f and g is established. It is shown that the changes in f do not cause any smearing of the singularities of g. Results of numerical experiments are presented.
Richard Ketcham (University of Texas - Austin) Measuring features in volumetric data sets using Blob3D
Abstract: Blob3D is a software project begun at the University of Texas at Austin in 1999 for facilitating measurements of discrete features of interest in volumetric data sets. It is designed in particular to deal with cases where features are touching or impinging, and to allow up to tens of thousands of features to be processed in a reasonable amount of time. Processing is broken into three stages: segmentation of a phase of interest, separation of touching objects, and extraction of measurements from the interpreted volume. For each stage a variety of three-dimensional algorithms have been created that account for vagaries of CT data, and program design is intended to enable relatively straightforward addition of new methods as they are developed. Separation is the most time-intensive step, as it utilizes manual and semi-automated methods that rely heavily on the user. This approach is most appropriate in many instances where the natural variation and complexity of the features require expert interpretation, but further automation is a future goal. Although designed in particular for geological applications using X-ray CT data, Blob3D is sufficiently general that it can be applied to other data types and in other fields.
Misha Kilmer (Tufts University) 3D Shape-based Image Reconstruction in Diffuse Optical Tomography
Abstract: In diffuse optical tomography (DOT), data is obtained by transmitting near-infrared light into a highly absorbing and scattering medium and then recording the photon flux. The goal is to use the diffuse optical data measured on the surface to reconstruct 3D images of the absorption and ``reduced scattering" functions in the medium. In the case of breast tissue imaging, relative differences in the absorption and scattering may indicate the presence of a tumor or other anomaly within the region of interest. If one considers the image value in each voxel as an unknown, the imaging problem is ill-posed and severely underdetermined. Traditional forms of regularization (e.g. Tikhonov) are computationally cumbersome, especially when one factors in the cost of computing associated appropriate regularization parameter. Instead, we model the absorption and reduced scattering functions as (nearly) piece-wise continuous functions, where the boundries of the ``hot spots" of activity in the images are modeled explicitly by simple geometric shapes, or boundaries of special level sets, that can be expressed in terms of only a few parameters. The background is assumed to be either homogeneous or expressible in some known set of basis functions. Our model has the effect of greatly reducing the dimension of the search space thereby regularizing the problem and making the image recovery problem more computationally tractable. Numerical experiments on synthetic data will be used to show the potential of this approach.
Seongjai Kim (Mississippi State University) Zoomable PDEs
Abstract: The presentation introduces edge-forming schemes for image zooming by arbitrary magnification factors. Image zooming via conventional interpolation methods often produces the so-called checkerboard effect, in particular, when the magnification factor is large. In order to remove the artifact and to form reliable edges, a nonlinear convex-concave model and its numerical algorithm are suggested along with anisotropic edge-forming numerical schemes. The algorithm is analyzed for stability and choices of parameters. It has been numerically verified that the resulting algorithm can form clear edges in 2 to 3 iterations of a linearized ADI method. Various results are given to show effectiveness and reliability of the algorithm, for both gray-scale and color images. This is a joint work with Dr. Youngjoon Cha.
Peter Kuchment (Texas A & M University) On mathematics of thermoacoustic imaging
Abstract: Joint with Gaik Ambartsoumian. In thermoacoustic tomography TAT (sometimes called TCT), one triggers an ultrasound signal from the medium by radiating it with a short EM pulse. Mathematically speaking, under ideal conditions, the imaging problem boils down to inversion of a spherical Radon transform. The talk will survey known results and open problems in this area.
Chunming Li (Vanderbilt University Institute of Imaging Science) Active Contours with Local Binary Fitting Energy
Abstract: In this paper, we propose a novel region-based active contour model for image segmentation with a variational level set formulation. The basic idea of our method is to localize the fitting energy functional in Chan and Vese's active contour model without edges. We first introduce a local binary fitting energy functional on the contour and two fitting functions. Then, a global fitting energy is defined as the integral of the local fitting energy over the image domain. This energy functional is further incorporated into a variational level set formulation without reinitialization. Therefore, our model has no need for reinitialization. Due to the local binary fitting energy in the proposed active contour model, our method is able to segment images with non-homogeneous regions and multiple distinct means, and therefore has much broader applications than the original Chan-Vese model. Our method has been successfully applied to blood vessel segmentation, which shows unique advantages over the previous models.
Hyeona Lim (Mississippi State University) Method of Background Subtraction for Medical Image Segmentation
Abstract: Medical images can involve high levels of noise and unclear edges and therefore their segmentation is often challenging. In this presentation, we consider the method of background subtraction (MBS) in order to minimize difficulties arising in the application of segmentation methods to medical imagery. When an appropriate background is subtracted from the given image, the residue can be considered as a perturbation of a binary image, for which most segmentation methods can detect desired edges effectively. New strategies are presented for the computation of the background and tested along with active contour models. Various numerical examples are presented to show effectiveness of the MBS for segmentation of medical imagery. The method can be extended to an efficient surface detection of 3-D medical images.
Thomas H. Mareci (University of Florida) Imaging Translational Water Diffusion with Magnetic Resonance for Fiber Mapping in the Central Nervous System
Abstract: Work in collaboration with Evren Ozarslan of the National Institutes of Health and Baba Vemuri of the University of Florida. Magnetic resonance can be used to measure the rate and direction of molecular translational diffusion. Combining this diffusion measurement with magnetic resonance imaging methods allows the visualization of 3D motion of molecules in structured environments, like biological tissue. In its simplest form, the 3D measure of diffusion can be modeled as a real, symmetry rank-2 tensor of diffusion rate and direction at each image voxel. At a minimum, this model requires seven unique measurements of diffusion to fit the model (Basser, et al., J Magn Reson 1994;B:247–254). The resulting rank-2 tensor can be used to visualize diffusion as an ellipsoid at each voxel and fiber connections can be inferred by connecting the path, defined by the long axis (principle eigenvector) of the ellipse, passing through each voxel. However, the rank-2 model of diffusion fails to accurately represent diffusion in complex structured environments, like nervous tissue with many crossing fibers. This limitation can be overcome by extending the angular resolution of diffusion measurements (Tuch, et al., Proceedings of the 7th Annual Meeting of Inter Soc Magn Reson Med, Philadelphia, 1999. p 321.) and by modeling the diffusion with higher rank tensors (Ozarslan et al., Magn. Reson. Med. 2003; 50:955-965 & Magn. Reson. Med. 2005;53;866-876). At each voxel in this more complete model, the 3D diffusion is represented by an "orientation distribution function" (ODF) indicating the probability of diffusion rate and direction. The diffusion ODF can be used to infer fiber connectivity but the issue of probable path selection remains a challenge. Plus the chosen procedure for path selection will influence with the level of resolution required for the measurements. In this presentation, methods of diffusion measurement and examples of diffusion-weighted magnetic resonance images from brain and spinal cord will be presented to illustrate the potential and challenges for path selecting leading to fiber mapping in the central nervous system.
Ozan Oktem (Sidec Technologies AB) Electron tomography. A short overview of methods and challenges
Abstract: Already in 1968 one recognized that the transmission electron microscope could be used in a tomographic setting as a tool for structure determination of macromolecules. However, its usage in mainstream structural biology has been limited and the reason is mostly due to the incomplete data problems that leads to severe ill-posedness of the inverse problem. Despite these problems its importance is beginning to increase, especially in drug discovery. In order to understand the difficulties of electron tomography one needs to properly formulate the forward problem that models the measured intensity in the microscope. The electron-specimen interaction is modelled as a diffraction tomography problem and the picture is completed by adding a description of the optical system of the transmission electron microscope. For weakly scattering specimens one can further simplify the forward model by employing the first order Born approximation which enables us to explicitly express the forward operator in terms of the propagation operator from diffraction tomography acting on the specimen convolved with a point spread function, derived from the optics in the microscope. We next turn to the algorithmic and mathematical difficulties that one faces in dealing with the resulting inverse problem, especially the incomplete data problems that leads to severe ill-posedness. Even though we briefly mention single particle methods, our focus is will be on electron tomography of general weakly scattering specimens and we mention some of the progress that has been made in the field. Finally, if time permits, we provide some examples of reconstructions from electron tomography and demonstrate some of the biological interpretations that one can make.
Sarah K. Patch (University of Wisconsin - Milwaukee) Thermoacoustic Tomography - Reconstruction of Data Measured under Clinical Constraints
Abstract: Thermoacoustic tomography (TCT) is a hybrid imaging technique that has been proposed as an alternative to xray mammography. Ideally, electromagnetic (EM) energy is deposited into the breast tissue uniformly in space, but impulsively in time. This heats the tissue causing thermal expansion. Cancerous masses absorb more energy than healthy tissue, creating a pressure wave, which is detected by standard ultrasound transducers placed on the surface of a hemisphere surrounding the breast. Assuming constant sound speed and zero attenuation, the data represent integrals of the tissue's EM absorptivity over spheres centered about the receivers (ultrasound transducers). The inversion problem for TCT is therefore to recover the EM absorptivity from integrals over spheres centered on a hemisphere. We present an inversion formula for the complete data case, where integrals are measured for centers on the entire sphere. We discuss differences between ideal and clinically measurable TCT data and options for accurately reconstructing the latter.
Henning F. Poulsen (Riso National Laboratory) Grain maps and grain dynamics — a reconstruction challenge
Abstract: Crystalline materials such as most metals, ceramics, rocks, drugs, and bones are composed of a 3D space-filling network of small crystallites r the grains. The geometry of this network governs a range of physical properties such as hardness and lifetime before failure. Our group has pursued an experimental method—3DXRD— which for the first time enable structural characterisation of the grains in 3D. Furthermore, changes in grain morphology can be followed during typical industrial processes such as annealing or deformation.

3DXRD is based on reconstruction principles. In comparison to conventional tomography the use of higher dimensional spaces is required. The projections are subject to group symmetry and their number is inherently limited. The grains exhibit a number of geometric properties which can be utilised. Furthermore the problem at hand can be reformulated in terms of both vector-type and scalar-type reconstructions. In conjunction these effects make 3DXRD reconstruction mathematically challenging.

The 3DXRD method will be presented with a few applications. The algorithms developed so far—for simplifying cases—will be summarised with focus on continuous reconstruction methods.

Eric Todd Quinto (Tufts University) An introduction to the mathematics of tomography
Abstract: The speaker will provide an overview of the Radon transform, showing its relationship with X-ray tomography and other tomographic problems. He will also describe the filtered back projection inversion formula and contrast it with Lambda tomography. Finally, he plans to give an elementary introduction to microlocal analysis and its implications for limited data tomography. Sample reconstructions (tomography pictures) will be provided to illustrate the ideas.
Gregory J. Randall (Universidad de la Republica) An Active Regions approach for the segmentation of 3D biological tissue
Abstract: Joint work with Juan Cardelino and Marcelo Bertalmio. Some of the most succesful algorithms for the automated segmentation of images use an Active Regions approach, where a curve is evolved so as to maximize the disparity of its interior and exterior. But these techniques require the manual selection of several parameters, which make impractical the work with long image sequences or with a very dissimilar set of sequences. Unfortunately this is precisely the case with 3D biological image sequences. In this work we improve on previous Active Regions algorithms in two aspects: by introducing a way to compute and update the optimum weights for the different channels involved (color, texture, etc.) and by estimating if the moving curve has lost any object so as to launch a re-initialization step. Our method is shown to outperform previous approaches. Several examples of biological image sequences, quite long and different among themselves, are presented.
Walter Richardson (University of Texas - San Antonio) Sobolev gradients and negative norms for image decomposition
Abstract: The use of Sobolev gradients and negative norms has proven to be a very useful preconditioning strategy for a variety of problems from mechanics and CFD, including transonic flow, minimal surface, and Ginzburg-Landau. We summarize results of applying this methodology in a variational approach for image decomposition f=u+v+w.
Erik L. Ritman (Mayo Clinic) Dual-Modality Micro-CT with Poly-Capillary X-ray Optics
Abstract: Conventional attenuation-based x-ray micro-CT is limited in terms of the image contrast it can convey for differentiating different tissue components, spaces and functions. Multi-modality imaging (e.g., radionuclide emission and/or x-ray scatter) can expand the information that can be obtained about those tissue aspects, but a challenge is accurate co-registration of the multiple images needed for the CT image data to be used to enhance the other modality's specificity. Poly-capillary optics consist of bundles of hollow glass capillaries (nominally 25µm in lumen diameter) which can "bend" x-rays or gamma rays by virtue of reflection of the photons within those capillaries. This approach serves both to exclude unwanted radiation (i.e., collimates the radiation) and to allow passage of radiation along accurately described paths - either parallel or focused. As both x-rays from an external x-ray source and from gamma ray emitters and x-ray scatterers within an object can be imaged with this approach, the images from these three modalities are perfectly co-registered. This allows use of the x-ray image to provide for attenuation correction of the internally generated radiation, as well as restricting that emission to specific anatomic structures and spaces by virtue of a priori physiological knowledge.
Partha S. Routh (Boise State University) Total variation imaging followed by spectral decomposition using continuous wavelet transform
Abstract: In general geophysical images provide two kinds of information: (a) structural images of discontinuities that define various lithology units and (b) physical property distribution within these units. Depending on the resolution of the geophysical survey, large scale changes can usually be detected that are often correlated with stratigraphic architecture of the subsurface. Knowledge of these architectural elements provides information about subsurface. Total variation (TV) regularization is one possibility to preserve discontinuity in the images. Another goal is to interpret these images is to obtain features that have varying scale information. Wavelets have the attractive quality of being able to resolve scale information in signal or data set. Moreover, heterogeneity produces non-stationary signal that can be effectively analyzed using wavelets due to its localization property. In this work we will present a new methodology for computing a time-frequency map for non-stationary signals using the continuous wavelet transform (CWT) that is more advantageous than conventional method of producing a time-frequency map using the Short Time Fourier Transform (STFT). This map is generated by transforming the time-scale map by taking the Fourier transform of the inverse CWT to produce a time-frequency map. We refer to such a map as the time-frequency CWT (TFCWT). Imaging using total variation regularization operator followed by spectral decomposition using TFCWT can be used as an effective interpretive tool.
Guillermo R. Sapiro (University of Minnesota) 3D segmentation in tomography
Abstract: In this talk I will describe recent results in the segmentation of relevant structures in electron tomography. We have developed novel techniques based on PDEs to work with this extremely hard data. I will describe the problem and the proposed solution, both at a tutorial level for a general audience. This is joint work with A. Bartesaghi and S. Subramaniam from NCI at NIH.
Martin Welk (University of the Saarland) Structure-Preserving Filtering of DT-MRI Data: PDE and Discrete Approaches
Abstract: Joint work with: Joachim Weickert, Christian Feddern, Bernhard Burgeth, Christoph Schnoerr, Florian Becker.

Curvature-driven PDE filters like mean-curvature motion (MCM), and median filters are well-studied as structure-preserving filters for grey-value images. They are related via a remarkable approximation result by Guichard and Morel.

We show generalisations of both types of filters to multivariate, specifically matrix-valued images. We discuss properties and algorithmic aspects, and demonstrate their usefulness for the filtering of diffusion-tensor data.

Graham A. Winbow (ExxonMobil) Common reflection angle imaging
Abstract: Common reflection angle migration (CRAM) is a computationally efficient ray-based seismic imaging technology developed at ExxonMobil which, as its name implies, enables us to form images of the subsurface in which all reflection events are imaged at the same reflection angle. It is most useful in complex imaging situations, such as beneath salt masses where signal/noise is a key issue and CRAM often enables us to separate signal and noise by comparing and contrasting different common reflection angle volumes. Our poster shows a recent example of how this works in practice.
Alex Zamyatin (Bio-Imaging Research) Sinogram decomposition for fan beam transform and its applications
Abstract: Recently several research groups independently proposed a sinogram decomposition approach for different problems in medical imaging. Sinogram is the set of projections of the reconstructed object. The main idea is to treat a sinogram as a family of the sinogram curves (s-curves). Each s-curve is obtained by tracing a single object point in the sinogram. There are many operators that can be defined on a the space of s-curves: backprojection (sum), minimum/maximum, etc. Therefore, the sinogram decomposition approach can be used in many applications: reconstruction from noisy data, sinogram completion for truncation correction and field-of-view extension, and artifact correction. In this poster we will derive equations of s-curves in fan-beam geometry, native for medical CT scanners, parameterize the family of s-curves through a given sinogram pixel, and consider some of the applications, where we suggest ways for estimation of missing data using this approach.
Visitors in Residence
Akram Aldroubi Vanderbilt University 1/10/2006 - 1/13/2006
Aisha Alwehebi Mississippi State University 1/8/2006 - 1/12/2006
Gaik Ambartsoumian Texas A & M University 1/8/2006 - 1/12/2006
Jung-Ha An University of Minnesota 9/1/2005 - 8/31/2007
Mark A. Anastasio Illinois Institute of Technology 1/8/2006 - 1/11/2006
Fredrik Andersson Lund University 1/8/2006 - 1/12/2006
Douglas N. Arnold University of Minnesota 7/15/2001 - 8/31/2006
Donald G. Aronson University of Minnesota 9/1/2002 - 8/31/2006
Heath Barnett Louisiana State University 1/8/2006 - 1/12/2006
Evgeniy Bart University of Minnesota 9/1/2005 - 8/31/2007
Aleksei Beltukov University of the Pacific 1/8/2006 - 1/12/2006
Francisco Blanco-Silva Purdue University 9/1/2005 - 6/30/2006
Edward Howard Bosch National Geospatial Intelligence Agency 1/8/2006 - 1/13/2006
Oliver Brunke University of Bremen 1/7/2006 - 1/13/2006
Les G. Butler Louisiana State University 1/4/2006 - 1/15/2006
Emmanuel J. Candes California Institute of Technology 1/8/2006 - 1/12/2006
Youngjoon Cha Sejong University 1/8/2006 - 1/12/2006
Kyle Champley Oregon State University 1/8/2006 - 1/13/2006
Qianyong Chen University of Minnesota 9/1/2004 - 8/31/2006
Jens Gerlach Christensen Louisiana State University 1/7/2006 - 1/13/2006
Ivan Christov Texas A & M University 1/8/2006 - 1/12/2006
Charles Collins University of Tennessee 1/8/2006 - 1/12/2006
Steven Benjamin Damelin Georgia Southern University 8/9/2005 - 6/30/2006
Susanna Dann Louisiana State University 1/8/2006 - 1/12/2006
David Deerfield Pittsburgh Supercomputing Center 1/8/2006 - 1/12/2006
Yves Defrenne University of Minnesota 1/9/2006 - 1/12/2006
Brian DiDonna University of Minnesota 9/1/2004 - 8/31/2006
Boris Aharon Efros Ben-Gurion University of the Negev 1/8/2006 - 1/13/2006
Selim Esedoglu University of Michigan 1/8/2006 - 1/14/2006
Adel Faridani Oregon State University 1/8/2006 - 1/12/2006
Alex Gittens University of Houston 1/8/2006 - 1/12/2006
Natalia Grinberg Universitat Karlsruhe 1/4/2006 - 1/31/2006
Changfeng Gui University of Connecticut 9/12/2005 - 6/30/2006
Jooyoung Hahn KAIST 8/26/2005 - 7/31/2006
Kyunmgin Ham Louisiana State University 1/8/2006 - 1/13/2006
Hazem Hamdan University of Minnesota 1/9/2006 - 1/12/2006
Gloria Haro Ortega University of Minnesota 9/1/2005 - 8/31/2007
Gabor T. Herman City University of New York 1/8/2006 - 1/13/2006
Michael Hofer Vienna University of Technology 1/9/2006 - 1/12/2006
Kathleen Hoffman University of Maryland - Baltimore County 1/8/2006 - 1/13/2006
Imitaz Hossain Louisiana State University 1/8/2006 - 1/12/2006
Xiang Huang University of Connecticut 9/1/2005 - 6/30/2006
Steven Izen Case Western Reserve University 1/8/2006 - 1/12/2006
Saurabh Jain University of Houston 1/8/2006 - 1/12/2006
Sookyung Joo University of Minnesota 9/1/2004 - 8/31/2006
George Kamberov Stevens Institute of Technology 1/8/2006 - 1/12/2006
Sung Ha Kang University of Kentucky 1/1/2006 - 5/31/2006
Chiu Yen Kao University of Minnesota 9/1/2004 - 8/31/2006
Alexander Katsevich University of Central Florida 1/10/2006 - 1/12/2006
Richard Ketcham University of Texas - Austin 1/8/2006 - 1/12/2006
Seongjai Kim Mississippi State University 1/8/2006 - 1/12/2006
SungWan Kim Yonsei University 1/8/2006 - 1/13/2006
Jens Klein Rensselaer Polytechnic Institute 1/8/2006 - 1/12/2006
Carl E. Krill University of Ulm 1/8/2006 - 1/13/2006
Peter Kuchment Texas A & M University 1/8/2006 - 1/11/2006
Matthias Kurzke University of Minnesota 9/1/2004 - 8/31/2006
Song-Hwa Kwon University of Minnesota 8/30/2005 - 8/31/2007
David Larson Texas A & M University 1/8/2006 - 1/12/2006
Chang-Ock Lee KAIST 8/1/2005 - 7/31/2006
Nam-Yong Lee Inje University 1/20/2006 - 2/11/2006
Ofer Levi Ben-Gurion University of the Negev 1/8/2006 - 1/13/2006
Stacey E. Levine Duquesne University 1/3/2006 - 6/30/2006
Debra Lewis University of Minnesota 7/15/2004 - 8/31/2006
Chunming Li Vanderbilt University 1/9/2006 - 1/12/2006
Hstau Liao University of Minnesota 9/2/2005 - 8/31/2007
Hyeona Lim Mississippi State University 1/8/2006 - 1/12/2006
W. Brent Lindquist State University of New York - Stony Brook 1/8/2006 - 1/12/2006
Jundong Liu Ohio University - Athens 1/8/2006 - 1/11/2006
Bradley J. Lucier Purdue University 8/15/2005 - 6/30/2006
Michael W. Mahoney Yahoo 1/8/2006 - 1/13/2006
Alison Malcolm University of Minnesota 9/1/2005 - 8/31/2006
Thomas H. Mareci University of Florida 1/8/2006 - 1/12/2006
Dionisios Margetis Massachusetts Institute of Technology 1/17/2006 - 1/21/2006
Peter R. Massopust Tuboscope Pipeline Services 1/7/2006 - 1/12/2006
Frank Natterer Universitaet Muenster 1/7/2006 - 1/13/2006
Ozan Oktem Sidec Technologies AB 1/8/2006 - 1/12/2006
Gestur Olafsson Louisiana State University 1/8/2006 - 1/13/2006
Peter J. Olver University of Minnesota 9/1/2005 - 6/30/2006
Winston Ou University of Minnesota 9/1/2005 - 1/13/2006
Manos Papadakis University of Houston 1/8/2006 - 1/12/2006
Sarah K. Patch University of Wisconsin - Milwaukee 1/9/2006 - 1/12/2006
Peter Philip University of Minnesota 8/22/2004 - 8/31/2006
Henning F. Poulsen Riso National Laboratory 1/7/2006 - 1/12/2006
Eric Todd Quinto Tufts University 1/8/2006 - 1/13/2006
Gregory J. Randall Universidad de la Republica 8/18/2005 - 7/31/2006
Walter Richardson University of Texas - San Antonio 9/1/2005 - 6/30/2006
Erik L. Ritman Mayo Clinic 1/9/2006 - 1/11/2006
Juan Romero University of Houston 1/8/2006 - 1/12/2006
Partha S. Routh Boise State University 1/8/2006 - 1/14/2006
Hans Rullgard Stockholm University 1/8/2006 - 1/12/2006
Steven Ruuth Simon Fraser University 1/8/2006 - 1/14/2006
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
Jin Keun Seo Yonsei University 1/5/2006 - 6/5/2006
Ashish Khudasia Sharma Indian Institute of Technology 1/7/2006 - 1/13/2006
Tatiana Soleski University of Minnesota 9/1/2005 - 8/31/2007
Peter Stiller Texas A & M University 1/8/2006 - 1/12/2006
Nathaniel Strawn Texas A & M University 1/8/2006 - 1/12/2006
Vladimir Sverak University of Minnesota 9/1/2005 - 6/30/2006
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
Eric Weber Iowa State University 1/8/2006 - 1/13/2006
Martin Welk University of the Saarland 12/5/2005 - 3/10/2006
Art Wetzel Pittsburgh Supercomputing Center 1/8/2006 - 1/12/2006
Thomas Neil Williams Mississippi State University 1/8/2006 - 1/12/2006
Graham A. Winbow ExxonMobil 1/8/2006 - 1/13/2006
Alex Zamyatin Bio-Imaging Research 1/9/2006 - 1/12/2006
Ofer Zeitouni University of Minnesota 9/1/2005 - 6/30/2006
Legend: Postdoc or Industrial Postdoc Long-term Visitor

Participating Institutions: Air Force Research Laboratory, Carnegie Mellon University, Consiglio Nazionale delle Ricerche, 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, 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, General Electric, General Motors, Honeywell, IBM, Johnson & Johnson, Lockheed Martin, Medtronic, Motorola, Schlumberger, Siemens, Telcordia