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IMA Newsletter #350

December 2005

2005-2006 Program

Imaging

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

News and Notes

2006–2007 New Directions Visiting Professors

The IMA is pleased to announce that the New Directions Visiting Professors for the 2006–2007 thematic program Applications of Algebraic Geometry will be Farhad Jafari of the University of Wyoming and Uwe Nagel of the University of Kentucky. New Directions Visiting Professorships provide an extraordinary opportunity for established mathematicians—typically mid-career faculty at US universities—to spend the academic year at the IMA. The Visiting Professors will enjoy an excellent research environment and stimulating scientific program, learning about and contributing to exciting new developments in algebraic geometry and a broad range of applications.

The New Directions program consists of the Visiting Professorships and the summer Short Courses. The IMA is currently accepting applications for the 2006 Short Course Biophysical Fluid Dynamics, June 19–30 (application deadline April 1, 2006).

IMA Events

IMA Annual Program Year Workshop

Integration of Sensing and Processing

December 5-9, 2005

Organizers: David J. Brady (Duke University), Dennis M. Healy Jr. (University of Maryland)

http://www.ima.umn.edu/imaging/W12.5-9.05/index.html

The last decade has seen unprecedented advances in the large-scale deployment, coordination, and monitoring of ubiquitous imaging systems in diverse and complex environments and serving a wide variety of purposes. Over the past 50 years a wide variety of novel imaging systems have been developed to work in different regions of the electromagnetic spectrum (from radio waves to X-rays) and which often differ significantly in format and function from the conventional visible imaging systems. These new imaging systems have been developed to serve a huge spectrum of applications ranging from astronomy, microscopy, medicine, and defense. Major government and industry research programs currently seek to develop and demonstrate a true revolution in imaging by implementing an intelligent integration of the advancing capabilities of the individual wavefront, detection, and processing subsystems.

Integration of Sensing and Processing (ISP) will leverage mathematical advances the way an earlier generation exploited mathematical ideas to create the foundations of Digital Signal Processing (DSP). However, in ISP advanced mathematics will play an even larger role, with an impact that now transcends the digital processor subsystem and extends across all sensor/exploitation subsystems. Fundamental advances in information science, optimization across subsystem boundaries, physical layer modeling, and real time adaptive control will be required to enable imaging systems integrating processing functionality directly into the front end of the sensor to support reduction of data dimensionality prior to digitization.

This workshop is being organized to address key issues in ISP, and will bring leading researchers in this emerging field, as well as potential contributors in other related areas.

Public Lecture

Dr. Philip J. Holmes

December 8, 2005

http://www.ima.umn.edu/2005-2006/PUB12.8.05/

The human brain contains about 100 billion neurons, each making about 1000 synaptic connections with other neurons. This huge dynamical system communicates with itself and its environment via electrical impulses called spikes. How is incoming information turned into spikes, and how do spikes create decisions and behaviors? Philip Holmes will show how mathematics helps us model and analyze such questions, involving events from single neural spikes to decisions that change our lives.
Schedule

Thursday, December 1

11:15a-12:15pSome mechanical models for earthquake sources, part IRobert Burridge (Massachusetts Institute of Technology)Lind Hall 409

Friday, December 2

11:15a-12:15pSome mechanical models for earthquake sources, part IIRobert Burridge (Massachusetts Institute of Technology)Lind Hall 409

Monday, December 5

8:30a-9:15aRegistration and coffeeEE/CS 3-176 W12.5-9.05
9:15a-9:30aWelcome to IMADouglas N. Arnold (University of Minnesota)EE/CS 3-180 W12.5-9.05
9:30a-10:00aOpening remarksDavid J. Brady (Duke University)
Dennis M. Healy Jr. (University of Maryland)
EE/CS 3-180 W12.5-9.05
10:00a-10:30acoffeeEE/CS 3-176 W12.5-9.05
10:30a-11:30aCompressive samplingEmmanuel J. Candes (California Institute of Technology)EE/CS 3-180 W12.5-9.05
11:30a-1:30plunch W12.5-9.05
1:30p-2:30pClosing the loop for ISP using performance predictionD. Gregory Arnold (Air Force Research Laboratory)EE/CS 3-180 W12.5-9.05
2:30p-3:00pcoffeeEE/CS 3-180 W12.5-9.05
3:00p-4:00pTarget detection using integrated hyper spectral sensing and processingRobert Muise (Lockheed Martin)EE/CS 3-180 W12.5-9.05
4:00p-4:30pSecond ChancesEE/CS 3-180 W12.5-9.05
4:40p-4:45pGroup photo W12.5-9.05
4:45p-6:00pPoster session and receptionLind Hall 400 W12.5-9.05
Modified Mumford-Shah model based simultaneous segmentation and registrationJung-Ha An (University of Minnesota)
Tomographic hyperspectral imaging without a missing-coneMichael E. Gehm (Duke University)
Self-localization in wireless sensor networks via manifold learningAlfred O. Hero III (University of Michigan)
The Method of Nonflat Time Evolution (MONTE) in PDE-based image restorationSeongjai Kim (Mississippi State University)
Direct reconstruction-segmentation, as motivated by electron microscopyHstau Liao (University of Minnesota)
A new generation of iterative transform algorithms for phase contrast tomography Russell Luke (University of Delaware)
Thermoacoustic TomographySarah K. Patch (University of Wisconsin - Milwaukee)
Sub-Pixel Image Registration and Quantitative Parameter ExtractionGustavo Kunde Rohde (Naval Research Laboratory)
Dimensionality reduction and divergence estimation for polarization-resolution trade in SAR imagesNitesh Shah (Raytheon Company)
Hyperspectral Image ProcessingMiguel Velez-Reyes (University of Puerto Rico at Mayaguez)
Smaller Infrared Cameras via Superresolution Image ReconstructionRebecca Willett (Duke University)

Tuesday, December 6

8:30a-9:00acoffeeEE/CS 3-176 W12.5-9.05
9:00a-10:00aIntegration of intrinsic geometries of data into the sensing and processing streamsRonald Raphael Coifman (Yale University)EE/CS 3-180 W12.5-9.05
10:00a-10:30acoffeeEE/CS 3-176 W12.5-9.05
10:30a-11:30aData fusion and multi-cue data matching using diffusion mapsStephane Lafon (Google)EE/CS 3-180 W12.5-9.05
11:30a-1:30plunch W12.5-9.05
1:30p-2:30pOn the role of the conditionality principle in dimensionality reductionCarey Priebe (John Hopkins University)EE/CS 3-180 W12.5-9.05
2:30p-3:00pcoffeeEE/CS 3-176 W12.5-9.05
3:00p-4:00pMulti-sensor adaptive ISPLawrence Carin (Duke University)EE/CS 3-180 W12.5-9.05
4:00p-4:30pSecond ChancesEE/CS 3-180 W12.5-9.05

Wednesday, December 7

8:30a-9:00acoffeeEE/CS 3-176 W12.5-9.05
9:00a-10:00aThe Richardson-Lucy algorithmRichard E. Blahut (University of Illinois - Urbana-Champaign)EE/CS 3-180 W12.5-9.05
10:00a-10:30acoffeeEE/CS 3-176 W12.5-9.05
10:30a-11:30aImaging without an imaging systemJames R. Fienup (University of Rochester)EE/CS 3-180 W12.5-9.05
11:30a-1:30plunch W12.5-9.05
1:30p-2:30pShaping light waves in three dimensions for integrated computational imagingRafael Piestun (University of Colorado)EE/CS 3-180 W12.5-9.05
2:30p-3:00pcoffeeEE/CS 3-176 W12.5-9.05
3:00p-4:00pCompressive optical spectroscopyDavid J. Brady (Duke University)EE/CS 3-180 W12.5-9.05
4:00p-4:30pSecond ChancesEE/CS 3-180 W12.5-9.05
4:30p-5:45pPoster session (same posters as on Monday)Lind Hall 400 W12.5-9.05
6:30p-8:00pWorkshop dinnerGardens of Salonika W12.5-9.05

Thursday, December 8

8:30a-9:00acoffeeEE/CS 3-176 W12.5-9.05
9:00a-10:00a Dimensionality reduction for integrated sensing and processingAlfred O. Hero III (University of Michigan)EE/CS 3-180 W12.5-9.05
10:00a-10:30acoffeeEE/CS 3-176 W12.5-9.05
10:30a-11:30aWavelets in biomedical data analysis: Scaling and functional design in applicationsBrani Vidakovic (Georgia Institute of Technology)EE/CS 3-180 W12.5-9.05
11:30a-1:30plunch W12.5-9.05
1:30p-2:30pActive learning vs. compressed sensingRobert Nowak (University of Wisconsin - Madison)EE/CS 3-180 W12.5-9.05
2:30p-3:30pImaging brain activity,and chemistry using high magnetic fieldsKamil Ugurbil (University of Minnesota)EE/CS 3-180 W12.5-9.05
7:00p-8:00pIMA Public Lecture: Does Math Matter to Brain Matter?Philip J. Holmes (Princeton University)Willey Hall 125 W12.5-9.05

Friday, December 9

8:30a-9:00acoffeeEE/CS 3-176 W12.5-9.05
9:00a-10:00aConstrained sensor localization and my wish list on integrated video processingGuillermo R. Sapiro (University of Minnesota)EE/CS 3-180 W12.5-9.05
10:00a-10:30acoffeeEE/CS 3-176 W12.5-9.05
10:30a-11:30aThe geometry of colorSteven W. Zucker (Yale University)EE/CS 3-180 W12.5-9.05
11:30a-12:00pSecond ChancesEE/CS 3-180 W12.5-9.05

Wednesday, December 14

11:15a-12:15pTBAAnne Gelb (Arizona State University)Lind Hall 409
Abstracts
a
Jung-Ha An (University of Minnesota) Modified Mumford-Shah model based simultaneous segmentation and registration
Abstract: A new variational region based model for a simultaneous image segmentation and registration using modified Mumford-Shah technique is suggested. The purpose of the model is segment and register given images simultaneously utilizing modified Mumford-Shah technique and region intensity values. The segmentation is obtained by minimizing modified Mumford-Shah model. A global rigid registration is assisted by the segmentation information and region intensity values. The numerical experiments of the proposed model are tested against synthetic and simulated human brain MRI images. The experimental results show the effectiveness of the model in detecting the boundaries of the given objects and registering given images simultaneously.
D. Gregory Arnold (Air Force Research Laboratory) Closing the loop for ISP using performance prediction
Abstract: ATR Theory, especially the performance prediction aspects, are fundamental to integrated sensing and processing. Offline and online prediction and feedback are essential processing tools for assessing which sensing actions will likely provide the most information. I'll discuss the overlap between Active Vision, ATR Theory, and ISP and highlight relevant research issues along the way.
David J. Brady (Duke University) Compressive optical spectroscopy
Abstract: Optical spectroscopy offers an ideal area for testing and development of compressive sensing systems. Measurement costs can be high, generalized sampling strategies are easily implemented and prior information and feature specific tasks are common. This talk describes experimental and conceptual studies of compressive spectroscopy in the DISP group over the past several years.
Robert Burridge (Massachusetts Institute of Technology) Some mechanical models for earthquake sources, part I
Abstract: We describe some early models for earthquake sources starting with the double-couple point source and ending with the still idealized two-dimensional repetitive fracture mechanical model for frictional strike slip on a vertical fault embedded in a viscoelastic half space. Except for the simple double-couple source, the models have in common the feature that a fault (or its analog) is held in equilibrium until increasing tangential traction breaks the static limiting friction. Once static friction is broken sliding occurs and is resisted by the smaller dynamic friction. It is the instability induced by this drop in friction that leads to the characteristic earthquake-like behaviour. The driving force during the motion is the drop in traction from the initial traction to the lower traction dictated by dynamic friction. After sliding begins static friction plays no further role. Other phenomena of this type are the vibrations of strings of the violin and related instruments, the squealing of brakes, and the creaking of door hinges. In the musical examples the periodicity is dictated by resonance of the finite vibrating system, whereas in earthquakes the system is effectively infinite.

More specifically we consider the following models in order of increasing complexity. 1) The time-step, double-couple source, which is known to represent a source consisting of instantaneous (tangential) slip on a small region a fault embedded in an isotropic elastic medium. We illustrate the associated far-field radiation pattern and discuss the use of the double couple as an influence (Green's) function.
2) The spring and block model. This model in its simplest form consists of a chain of blocks connected by springs. The blocks rest on a rough table and the chain of blocks is drawn along slowly by an irresistible constant-velocity drive at the leading end of the spring at the (front) end of the chain. The blocks are observed to move in a jerky fashion reminiscent of earthquakes. In fact this system emulates many features of earthquakes. If we interpret each jerk as an earthquake the number of blocks slipping in one event may represent the extent of rupture at the source. The magnitude may be represented by the drop in the potential energy of the springs (or its logarithm) and the frequency-magnitude statistics are reminiscent of the Gutenberg-Richter relation. While this model can be set up as a simple bench-top demonstration, computational models simulating it and its generalizations are richer and lend themselves to more precise analysis. For instance, by replacing the frictional resistance by a viscous resistance aftershock sequences may be generated and also analyzed statistically. The chain of blocks may be replaced by a two dimensional array of blocks, and the system may be driven in more complicated ways more like a discretization of a sliding fault driven by relative motion of the halfspaces on either side of it. Other forms may be imagined in which several faults interact.
3) A numerical simulation of an earthquake model in which the region of slip is specified and the problem is to find the amount of slip. We discuss the numerical solution of the singular integral equation and in particular the discretization of the non-integrable kernel and show illustrations of the displacements obtained both for antiplane and for plane strain.
4) An analytic solution of the two-dimensional problem of strike slip on a vertical fault driven an initial shear stress. The initial configuration is held in equilibrium by static friction until the traction at some point on the fault exceeds the static limit of friction. Thereafter a region of slip expands about the point of nucleation running initially with the shearwave speed both up and down. The downward-travelling 'crack' tip slows to a subsonic speed owing to the increasing friction with depth, and slows to a stop. The complete sliding motion also stops around this time. The full sliding displacement is calculated by solving analytically certain Abel integral equations which arise from specializing the Green function for the two-dimensional wave equation to the fault plane. The far field pulse shapes are calculated and a very strong breakout phase is identified which dominates the pulse in direction close to vertically down. The subsonic part of the downward travelling 'crack' edge is interrupted by this stopping phase and runs again briefly at the shearwave speed. This work was influenced by papers of Boris Kostrov from the 1960s.
5) A repetitive earthquake model consisting of a source of the previous type embedded in a viscoelastic halfspace driven by a slow viscous shear flow at infinity. The time scale for relaxation of the viscoelastic medium is very much greater than the time scale of the Burridge-Halliday mechanism, i.e.the time it takes for elastic waves to traverse the source region. The relative magnitudes of static friction, dynamic friction, and the stress at infinity determine the ratio of the repetition rate to the time scale of the source mechanism. Unfortunately the world is not a two-dimensional halfspace undergoing antiplane shear and fault planes are not only much more complicated but we do not know the necessary parameters such as the preexisting stress fields and strength and properties of the material at the fault to predict earthquakes in a practically useful way. However, our statistical knowledge of seismicity can aid in assessing earthquake risk.

Emmanuel J. Candes (California Institute of Technology) Compressive sampling
Abstract: Conventional wisdom and common practice in acquisition and reconstruction of images or signals from frequency data follows the basic principle of the Nyquist density sampling theory. This principle states that to reconstruct an image/signal, the number of Fourier samples we need to acquire must match the desired resolution of the image/ signal, e.g. the number of pixels in the image. This talk introduces a newly emerged sampling theory which shows that this conventional wisdom is inaccurate. We show that perhaps surprisingly, images or signals of scientific interest can be recovered accurately and sometimes even exactly from a limited number of nonadaptive random measurements. In effect, the talk introduces a theory suggesting ``the possibility of compressed data acquisition protocols which perform as if it were possible to directly acquire just the important information about the image of interest.'' In other words, by collecting a comparably small number of measurements rather than pixel values, one could in principle reconstruct an image with essentially the same resolution as that one would obtain by measuring all the pixels, a phenomenon with far reaching implications. The reconstruction algorithms are very concrete, stable (in the sense that they degrade smoothly as the noise level increases) and practical; in fact, they only involve solving convenient convex optimization programs.
Lawrence Carin (Duke University) Multi-sensor adaptive ISP
Abstract: In this talk we examine the adaptive integration of sensing and signal processing in several settings. The underlying algorithms are based on information-theoretic active learning, as well as partially observable Markov decision processes (POMDPs). Modern techniques from machine learning are also considered. We concentrate on applying the underlying mathematics to specific practical sensing challenges, such as detection of buried landmines and unexploded ordnance, adaptive hyper-spectral sensing, and underwater acoustic sensing of concealed targets.
James R. Fienup (University of Rochester) Imaging without an imaging system
Abstract: One can trade off complexity in imaging system hardware and strict system tolerances for complexity in post-detection data processing. We describe an extreme example in this trade-off space: a coherent imaging approach that eliminates the imaging system hardware entirely (except for the detector array), relying on a phase retrieval algorithm to form the image in a computer. It has applications ranging from long-range imaging, such as ballistic missile defense, to microscopy.
Michael E. Gehm (Duke University) Tomographic hyperspectral imaging without a missing-cone
Abstract: A hyperspectral imager provides a 3-D data cube in which the spatial information (2-D) of an image is complemented by spectral information (1-D) about each spatial location. In a tomographic hyperspectral imager, the full 3-D data cube is reconstructed from a series of 2-D projections. In current systems, the projections are taken over a range of angles with respect to (and about) the wavelength-axis. Because a full range of angles cannot be measured, the system is undersampled in the Fourier domain (the so-called "missing cone"). We propose a new technique that is based upon our static, Hadamard-coded spectrometer. Using aperture coding allows us to measure projections through the data cube that are perpendicular to the wavelength-axis. With these projections, we can sample the a full angular range and avoid a "missing cone". As a result, the quality of the tomographic reconstruction should be significantly improved. We have constructed some preliminary instruments that provide proof-of-concept, and have begun working on more robust implementations.
Alfred O. Hero III (University of Michigan) Self-localization in wireless sensor networks via manifold learning
Abstract:Given a set of noisy pair-wise measurements in a wireless network of N sensors the self-localization problem is to estimate all N coordinates. We present a manifold learning approach to this problem using measured connectivity (within range or out-of-range) or received signal strength (RSS) btwn pairs of sensors. The advantage of such approaches is that they use dimensionality reduction to find robust estimates of the sensor locations without requireing a specific propagation model for the medium. Two methods are presented and compared: Distributed weighted multi-dimensional scaling (dwMDS) for range-based localization (J.A. Costa, N. Patwari, A.O. Hero, Distributed Weighted Multidimensional Scaling for Node Localization in Sensor Networks, ACM Journal on Sensor Networks, 2006) and Laplacian Eigenmaps (LE) for connectivity-based localization (N. Patwari and A.O. Hero Adaptive Neighborhoods for Manifold Learning-based Sensor Localization, IEEE SPAWC 05, June 2005).
Alfred O. Hero III (University of Michigan) Dimensionality reduction for integrated sensing and processing
Abstract: Dimensionality reduction methods have played a central role in exploration of parsimonious structural models, complexity regularization in inverse problems, and data compression. Examples are PCA, Laplacian eigenmaps, ISOMAP, and matching pursuits which attempt to fit a subspace to the data. For integrated sensing and processing (ISP) systems dimensionality reduction must go beyond simply fitting the data geometry. One must account for how dimension reduction will affect the performance of the processing task, e.g., image reconstruction or classification, and sensor scheduling, e.g., path planning or waveform design. We will present some thoughts and recent progress on dimensionality reduction for ISP.
Philip J. Holmes (Princeton University) IMA Public Lecture: Does Math Matter to Brain Matter?
Abstract: The human brain contains about 100 billion neurons, each making about 1000 synaptic connections with other neurons. This huge dynamical system communicates with itself and its environment via electrical impulses called spikes. How is incoming information turned into spikes, and how do spikes create decisions and behaviors? I will show how mathematics helps us model and analyze such questions, involving events from single neural spikes to decisions that change our lives.
Seongjai Kim (Mississippi State University) The Method of Nonflat Time Evolution (MONTE) in PDE-based image restoration
Abstract: Joint work with Youngjoon Cha. This article is concerned with effective numerical techniques for partial differential equation (PDE)-based image restoration. Numerical realizations of most PDE-based denoising models show a common drawback: loss of fine structures. In order to overcome the drawback, the article introduces a new time-stepping procedure, called the method of nonflat time evolution (MONTE), in which the timestep size is determined based on local image characteristics such as the curvature or the diffusion magnitude. The MONTE provides the PDE-based restoration models with an effective mechanism for the equalization of the net diffusion over a wide range of image frequency components. It can be easily applied to diverse evolutionary PDE-based restoration models and their spatial and temporal discretizations. It has been numerically verified that the MONTE results in a significant reduction in nonphysical dissipation and preserves fine structures such as edges and textures satisfactorily, while it removes the noise with an improved efficiency. Various numerical results are shown to confirm the claim.
Stephane Lafon (Google) Data fusion and multi-cue data matching using diffusion maps
Abstract: Data fusion and multi-cue data matching are fundamental tasks arising in a variety of systems that process large amounts of data. These tasks often rely on dimensionality reduction techniques that traditionally follow a data acquisition/reprocessing phase. In this talk, I will describe a powerful framework based on diffusions that can be used in order to learn the intrinsic geometry of data sets. These techniques allow to simultaneously handle data acquisition issues and data processing tasks. In particular, I will explain how we can use this set of tools in order to address three major challenges related to data fusion: 1) How to deal with data coming from sensors/sources sampled at different rates, and possibly at different times. We provide algorithms to obtain density-invariant descriptors (parametrization) of data sets. 2) How to integrate and combine information streams coming from different sensors into one representation of the data. The diffusion coordinates allow to learn the geometry of the data captured by each sensor independently, and then to combine the various representations into a unified description of the data. 3) How to do matching of data sets based on their intrinsic geometry. As an illustration, I will present numerical results on the integration of audio and video streams for lip-reading and speech recognition. Other examples will be more focused on imaging (multiscale data-driven image segmentation, image data sets alignment). This is joint work with R.R. Coifman, A. Glaser, Y. Keller and S.W. Zucker (Yale university).
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.

Joint work with Gabor T. Herman.

Russell Luke (University of Delaware) A new generation of iterative transform algorithms for phase contrast tomography
Abstract: In recent years, improvements in electromagnetic sources, detectors,optical components, and computational imaging have made it possible to achieve three-dimensional atomic-scale resolution using tomographic phase-contrast imaging techniques. These greater capabilities have placed a premium on improving the efficiency and stability of phase retrieval algorithms for recovering the missing phase information in diffraction observations. In some cases, so called direct methods suffice, but for large macromolecules and nonperiodic structures one must rely on numerical techniques for reconstructing the missing phase. This is the principal motivation of our work. We report on recent progress in algorithms for iterative phase retrieval. The theory of convex optimisation is used to develop and to gain insight into counterparts for the nonconvex problem of phase retrieval. We propose a relaxation ofaveraged alternating reflectors and determine the fundamental mathematical properties of the related operator in the convex case. Numerical studies support our theoretical observations and demonstrate the effectiveness of the newer generation of algorithms compared to the current state of the art.
Robert Muise (Lockheed Martin) Target detection using integrated hyper spectral sensing and processing
Abstract: Joint work with Abhijit Mahalanobis. The concept of Integrated Sensing and Processing (ISP) suggests that a sensor should collect data in a manner that is consistent with the end objective. Thus ISP seeks to minimize the collection of redundant data, reduce processing time and improve overall performance. We present a case study of ISP using a multi-spectral camera which allows the spatial resolution of the data to be varied in addition to selecting spectral bands that enable the detection of targets in background clutter. This paper is a preliminary description of work in progress, and illustrates the basic concepts by means of several examples.
Robert Nowak (University of Wisconsin - Madison) Active learning vs. compressed sensing
Abstract: Adaptive sampling, also called ``Active Learning'', uses information gleaned from previous measurements (e.g., feedback) to guide and focus the sampling process. Theoretical and experimental results have shown that adaptive sampling can dramatically outperform conventional non-adaptive sampling schemes. I will review some of the most encouraging theoretical results to date, and focus on new results regarding the capabilities of adaptive sampling methods for learning piecewise smooth functions. I will also contrast adaptive sampling with a new approach known as compressive sampling. Compressive sampling, or ``Compressed Sensing'', has generated a tremendous amount of excitement in the signal processing community and is seen as a strong competitor of adaptive procedures. Compressive sampling involves taking a relatively small number of non-traditional samples in the form of non-adaptive randomized projections that are capable of capturing the most salient information in a signal. I will compare adaptive and compressive sampling in noisy conditions, and show that in certain interesting cases both schemes are near-optimal. This result is remarkable since it is the first evidence of cases in which compressive sampling, which is non-adaptive, cannot be significantly outperformed by adaptive procedures, even in presence of noise. This is joint work with Rui Castro and Jarvis Haupt.
Sarah K. Patch (University of Wisconsin - Milwaukee) Thermoacoustic Tomography
Abstract: Abstract: pdf
Rafael Piestun (University of Colorado) Shaping light waves in three dimensions for integrated computational imaging
Abstract: Processing information at the sensor level can not only help reduce the amount of data acquired but also enhance the overall performance of the system. In this talk I will first present methods for shaping the three-dimensional response of an optical system. Then I will discuss how to integrate tailored optical responses with digital postprocessing algorithms to improve specific imaging tasks.
Carey Priebe (John Hopkins University) On the role of the conditionality principle in dimensionality reduction
Abstract: The idea of classifier construction via `Iterative Denoising' trees--- that is, by successively partitioning (at the internal nodes of the tree) a class-labeled training data set into ever-more homogeneous subsets without consideration of class labels, and only subsequently (at the leaves of the tree) using the available class-label information, while at each node (internal or leaf) choosing a dimensionality reduction appropriate to and specific to (the data falling in) that partition cell — may seem counter-intuitive but is in fact in (rough) accordance with Fisher's conditionality principle and can in fact provide performance superior to that of competing approaches. We describe the theory and application of these `Iterative Denoising' trees and illustrate their performance, and relate the ideas to `Integrated Sensing and Processing' and theorized thalamocortical brain circuit computation.
Gustavo Kunde Rohde (Naval Research Laboratory) Sub-Pixel Image Registration and Quantitative Parameter Extraction
Abstract: Registration methods are routinely used to automatically align images before quantitative parameters can be estimated from them. With many authors claiming sub-pixel accuracy in their registration procedures we show that the operations necessary for producing a series of images aligned to sub-pixel accuracy can significantly alter the statistical properties of the images. This, in turn, will have a significant effect on any quantitative parameters extracted from registered images. We look at the stochastic properties of B-spline interpolating basis functions of arbitrary degree and suggest means through which they can be used in quantitative parameter extraction from registered images. This study demonstrates by example the importance of integrating the stochastic properties of image sensors into image processing operations.
Guillermo R. Sapiro (University of Minnesota) Constrained sensor localization and my wish list on integrated video processing
Abstract: In this talk I will first show how to use simple and classical results from distance geometry to address the problem of sensor localization under physical constraints. Then I will move into presenting some recent results in video processing that I wish could be done at the sensor level. For example, I will show techniques that reduce the video data to only regions of interest. This will tremendously reduce transmission cost if done at the sensors level.

The work is in collaboration with members of my group (M. Mahmoudi and K. Patwardhan) and also in part with Honeywell (V. Morellas).

Nitesh Shah (Raytheon Company) Dimensionality reduction and divergence estimation for polarization-resolution trade in SAR images
Abstract: In the Integrated Sensing and Processing paradigm, agile sensors operating in a setting of limited power, bandwidth, etc. can receive feedback regarding sensor settings for subsequent data collection (sensor scheduling). In the system design phase, trades are often conducted balancing utility of different sensor settings or sensor configurations. Information-theoretic tools are useful for assisting in evaluating information gain in both of these settings. In particular, given fully polarimetric, measured synthetic aperture radar (SAR) images of two targets, we apply two dimensionality reduction techniques and a non-density-based divergence estimation approach to evaluate the relative target divergences over differences in effective spatial resolution and in the number of available polarization states. Divergence at the pre-classifier stage serves as a surrogate for target separability in an Automatic Target Recognition (ATR) setting, avoiding the extra layer of complexity induced by the choice of classifier and classifier parameter settings.
Miguel Velez-Reyes (University of Puerto Rico at Mayaguez) Hyperspectral Image Processing
Abstract:We will present some of our work in hyperspectral image processing. Two projects will be presented. In the first, we will focus on multiscale representation and the use of PDE methods for image representation. In the second, we will present the use of Positive Matrix Factorization for hyperspectral unmixing.
Brani Vidakovic (Georgia Institute of Technology) Wavelets in biomedical data analysis: Scaling and functional design in applications
Abstract: Measured bioresponses are often characterized by an intrinsic high frequency and strong persistent correlations inhibiting statistical modeling by the traditional techniques. The talk overviews two novel wavelet-based techniques for modeling such challenging data. Wavelet domains provide natural modeling environments for data that scale, as well as for data consisting of continuous n-dimensional functions. We briefly discuss technicalities and describe in detail two applications. First application deals with wavelet analysis of functional ANOVA (FANOVA) where the observations are curves coming from clinical research. The second application discusses classification methods based on wavelet-based measures of irregular scaling (multifractal spectra) applied on high frequency pupillary responses for patients with various eye pathologies.
Rebecca Willett (Duke University) Smaller Infrared Cameras via Superresolution Image Reconstruction
Abstract: Infrared camera systems can be make dramatically smaller by simultaneously collecting several low-resolution images with multiple narrow aperture lenses rather than collecting a single high- resolution image with one wide aperture lens. In this poster, we will describe this new infrared sensing system and a multiscale approach to processing the output of these novel sensors. The camera uses a 3x3 lenslet array having an effective focal length of 1.9 mm and we achieve image resolution comparable to a conventional single lens system having a focal length of 21mm, although the image dynamic range and linearity are reduced. The wavelet- based regularization utilized during image reconstruction reduces the appearance of artifacts while preserving key features such as edges and singularities. The processing method is very fast, making the integrated sensing and processing viable for both time- sensitive applications and massive collections of sensor outputs.

This is joint work with David Brady, Mohan Shankar and Andrew Portnoy.

Steven W. Zucker (Yale University) The geometry of color
Abstract: The representation of color for perception differs from the representation for displays. We consider the map from (r,g,b)-space to (Intensity, hue, saturation)-space, and show how this non-linear space is useful for sensing devices.
Visitors in Residence
Jung-Ha An University of Minnesota 9/1/2005 - 8/31/2007
D. Gregory Arnold Air Force Research Laboratory 12/5/2005 - 12/9/2005
Douglas N. Arnold University of Minnesota 7/15/2001 - 8/31/2006
Donald G. Aronson University of Minnesota 9/1/2002 - 8/31/2006
Amir Averbuch Tel Aviv University 12/4/2005 - 12/10/2005
Evgeniy Bart University of Minnesota 9/1/2005 - 8/31/2007
Richard E. Blahut University of Illinois - Urbana-Champaign 12/4/2005 - 12/7/2005
Francisco Blanco-Silva Purdue University 9/1/2005 - 6/30/2006
Brett Borden Naval Postgraduate School 10/1/2005 - 12/31/2005
Edward Howard Bosch National Geospatial Intelligence Agency 12/4/2005 - 12/10/2005
David J. Brady Duke University 9/18/2005 - 12/10/2005
Yoram Bresler University of Illinois - Urbana-Champaign 12/4/2005 - 12/10/2005
Robert Burridge Massachusetts Institute of Technology 9/1/2005 - 12/31/2005
Emmanuel J. Candes California Institute of Technology 12/4/2005 - 12/7/2005
Lawrence Carin Duke University 12/5/2005 - 12/9/2005
Qianyong Chen University of Minnesota 9/1/2004 - 8/31/2006
Margaret Cheney Rensselaer Polytechnic Institute 9/6/2005 - 12/31/2005
Marc P. Christensen Southern Methodist University 12/4/2005 - 12/9/2005
Giulio Ciraolo University degli Studi de Firenze 9/8/2005 - 12/23/2005
Douglas Cochran Arizona State University 12/4/2005 - 12/9/2005
Ronald Raphael Coifman Yale University 12/4/2005 - 12/9/2005
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
Marco F. Duarte Rice University 12/4/2005 - 12/10/2005
Yi Fang Rensselaer Polytechnic Institute 9/12/2005 - 12/20/2005
Michael A. Fiddy University of North Carolina - Charlotte 12/4/2005 - 12/9/2005
James R. Fienup University of Rochester 12/4/2005 - 12/9/2005
Jan Flusser Institute of Information Theory and Automation 12/3/2005 - 12/10/2005
Michael E. Gehm Duke University 12/4/2005 - 12/9/2005
Anne Gelb Arizona State University 11/28/2005 - 12/16/2005
Changfeng Gui University of Connecticut 9/12/2005 - 6/30/2006
Jooyoung Hahn KAIST 8/26/2005 - 7/31/2006
Mike Haney University of Delaware 12/4/2005 - 12/9/2005
John L. Harer Duke University 12/4/2005 - 12/8/2005
Gloria Haro Ortega University of Minnesota 9/1/2005 - 8/31/2007
Dennis M. Healy Jr. University of Maryland 12/4/2005 - 12/8/2005
Alfred O. Hero III University of Michigan 12/4/2005 - 12/9/2005
Philip J. Holmes Princeton University 12/7/2005 - 12/10/2005
Xiang Huang University of Connecticut 9/1/2005 - 6/30/2006
Shawn Hunt University of Puerto Rico at Mayaguez 12/4/2005 - 12/9/2005
Xiaoming Huo Georgia Institute of Technology 12/4/2005 - 12/9/2005
Ashoka Jayawardena University of New England, Australia 12/4/2005 - 12/10/2005
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
Seongjai Kim Mississippi State University 12/4/2005 - 12/9/2005
Timothy J. Klausutis Air Force Research Laboratory 12/5/2005 - 12/9/2005
Matthias Kurzke University of Minnesota 9/1/2004 - 8/31/2006
Song-Hwa Kwon University of Minnesota 8/30/2005 - 8/31/2007
Stephane Lafon Google 12/5/2005 - 12/7/2005
Chang-Ock Lee KAIST 8/1/2005 - 7/31/2006
Debra Lewis University of Minnesota 7/15/2004 - 8/31/2006
Hstau Liao University of Minnesota 9/2/2005 - 8/31/2007
Bradley J. Lucier Purdue University 8/15/2005 - 6/30/2006
Russell Luke University of Delaware 9/6/2005 - 12/31/2005
Abhijit Mahalanobis Lockheed Martin 12/4/2005 - 12/9/2005
Alison Malcolm University of Minnesota 9/1/2005 - 8/31/2006
George Michailidis University of Michigan 12/5/2005 - 12/9/2005
Steen Moeller University of Minnesota 12/5/2005 - 12/9/2005
Robert Muise Lockheed Martin 12/4/2005 - 12/9/2005
Shaileshkumar Musley Medtronic, Inc. 12/5/2005 - 12/9/2005
Robert Nowak University of Wisconsin - Madison 12/4/2005 - 12/9/2005
Jorge Ojeda Castaneda Universidad de las Americas, Puebla 12/4/2005 - 12/9/2005
Peter J. Olver University of Minnesota 9/1/2005 - 6/30/2006
Joseph A. O'Sullivan Washington University - St. Louis 12/4/2005 - 12/9/2005
Winston Ou University of Minnesota 9/1/2005 - 1/13/2006
Sarah K. Patch University of Wisconsin - Milwaukee 12/5/2005 - 12/9/2005
Peter Philip University of Minnesota 8/22/2004 - 8/31/2006
Rafael Piestun University of Colorado 12/4/2005 - 12/9/2005
Nikos P. Pitsianis Duke University 12/4/2005 - 12/9/2005
Carey Priebe John Hopkins University 12/5/2005 - 12/9/2005
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
Michael Dirk Robinson Ricoh Innovations 12/4/2005 - 12/9/2005
Gustavo Kunde Rohde Naval Research Laboratory 12/4/2005 - 12/9/2005
Fadil Santosa University of Minnesota 9/1/2005 - 6/30/2006
Guillermo R. Sapiro University of Minnesota 9/1/2005 - 6/30/2006
Alexander Sawchuk University of Southern California 12/4/2005 - 12/9/2005
Arnd Scheel University of Minnesota 7/15/2004 - 8/31/2006
Timothy Schulz Michigan Technological University 12/4/2005 - 12/9/2005
Tom L. Scofield Calvin College 9/1/2005 - 12/31/2005
Nitesh Shah Raytheon Company 12/4/2005 - 12/6/2005
Tatiana Soleski University of Minnesota 9/1/2005 - 8/31/2007
Vladimir Sverak University of Minnesota 9/1/2005 - 6/30/2006
Alan Thomas Clemson University 9/4/2005 - 12/17/2005
Carl Toews University of Minnesota 9/1/2005 - 8/31/2007
Kamil Ugurbil University of Minnesota 12/5/2005 - 12/9/2005
Miguel Velez-Reyes University of Puerto Rico at Mayaguez 12/5/2005 - 12/9/2005
Brani Vidakovic Georgia Institute of Technology 12/4/2005 - 12/8/2005
Jingyue Wang Purdue University 9/1/2005 - 6/30/2006
Xiaoqiang Wang University of Minnesota 9/1/2005 - 8/31/2007
Martin Welk University of the Saarland 12/5/2005 - 3/10/2006
Rebecca Willett Duke University 12/4/2005 - 12/9/2005
Hong Xiao University of California - Davis 12/5/2005 - 12/9/2005
Jeong-Rock Yoon Clemson University 9/6/2005 - 12/30/2005
Yuncheng You University of South Florida 12/4/2005 - 12/10/2005
Ofer Zeitouni University of Minnesota 9/1/2005 - 6/30/2006
Steven W. Zucker Yale University 12/7/2005 - 12/9/2005
Legend: Postdoc or Industrial Postdoc Long-term Visitor

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