DIMACS Center, Rutgers University, Piscataway, NJ

**Organizers:****Vivek Goyal**, Digital Fountain, v.goyal@ieee.org**Jelena Kovacevic**, Bell Labs, jelena@bell-labs.com

Title: On Frame Redundancy and Measure Functions

Richard Baraniuk, Rice UniversityTitle: Multiscale Edge Grammars for Image Modeling and Processing

Carlos Cabrelli and Ursula Molter, University of Buenos AiresTitle: Shift Invariant Spaces and Homogeneous Functions

Emmanual J. Candes, California Institute of Technology

Title: Geometric Multiscale Transforms, Space-Frequency Tilings, Minimum Total Variation Synthesis

The talk will introduce a wealth of new space-frequency tilings which lead to a new and large family of orthonormal bases for representing functions of two variables --images. This family of multiscale transforms is known under the name of the ridgelet packets library and includes systems such as ridgelets, curvelets and wavelets. Many of these bases have elements whose envelope is strongly aligned along specified `ridges' while displaying oscillatory components either along or across the main `ridge'.

In the second part of the talk, we propose to combine these new expansions with the Total Variation minimization principle for the reconstruction of an object whose curvelet coefficients are known only approximately: quantized, thresholded, noisy coefficients, etc. We set up a convex optimization problem and seek a reconstruction that has minimum Total Variation under the constraint that its coefficients do not exhibit a large discrepancy from the the data available on the coefficients of the unknown object.

We will present a series of numerical experiments which clearly demonstrate the remarkable potential of this new methodology for image compression, image reconstruction and image `de-noising.'

Peter G. Casazza, University of Missouri-ColumbiaTitle: Custom Building Tight Frames

Title: Harmonic Analysis and A/D Conversion

Oversampled A/D conversion, which is one of the most important practical source coding schemes, effectively performs irregular sampling of an input bandlimited signal with a precision equal to the resolution of the time-discretization of the conversion. In this talk we present an in-depth study of simple oversampled A/D conversion using techniques of nonharmonic Fourier analysis, and derive some new results on irregular sampling of bandlimited signals which are relevant for A/D conversion. We use these findings to construct a single-bit dithered A/D conversion scheme which attains exponential accuracy in the bit-rate. This is joint work with I.Daubechies and B.F.Logan

Ingrid Daubechies, Princeton UniversityTitle: Redundant representations for A/D conversion

Sigma-delta quantizers, used in A/D conversion of bandlimited signals, give one approach to quantize efficiently highly redundant samples. Part of the talk will discuss some mathematical properties of and questions raised by these schemes. In a second part of the talk, a different type of redundant representation will be discussed, based on so-called beta-expansions. The talk presents work by Ron DeVore, Sinan Gunturk, Nguyen Thao, Vinay Vaishampayan and Ozgur Yilmaz as well as the author.

Matt Fickus, Cornell UniversityTitle: Finite Normalized Tight Frames

Alyson Fletcher, University of California BerkeleyTitle: Wavelet Denoising by Recursive Cycle Spinning

Anna Gilbert, AT&T Labs - Research, Shannon LaboratoryTitle: Near-Optimal Sparse Fourier Representations via Sampling

Ramesh A. Gopinath, IBM T. J. Watson ResearchTitle: The Phaselet Transform - An Integral Redundancy Nearly Shift Invariant Wavelet Transform

Vivek K Goyal, Digital Fountain, Inc.Title: Theorems and Counterexamples in Transform Coding

C. Sinan Gunturk, Courant Institute of Mathematical Sciences, New York UniversityTitle: One-Bit Sigma-Delta Quantization with Exponential Accuracy

C. Heil, School of Mathematics, Georgia Institute of TechnologyRadu Balan, Siemens Corporate Research, Princeton, New JerseyPeter G. Casazza, Department of Mathematics, University of MissouriZeph Landau, Mathematical Sciences Research Institute

Nick Kingsbury and Tanya Reeves, Signal Processing Group, Department of Engineering, University of CambridgeTitle: Image Compression with Overcomplete Complex Wavelets using Iterative Projection

Ognyan Kounchev, Bulgarian Academy of Scineces / University of DuisburgHermann Render, University of Duisburg, GermanyTitle: Distributed Filters - Application of Polysplines to Image Processing

Jelena Kovacevic, Bell Labs, Lucent TechnologiesAurelie C. Lozano, MIT Media LabMike Andrews, Bell Labs, Lucent TechnologiesTitle: Quantized Frame Expansions in a Wireless Environment

Z. Landau, University of California, Berkeley

Stephane Mallat, Courant Institute, New York UniversityErwan Le Pennec, Ecole Polytechnique, FranceTitle: Sparse Geometrical Image Representations with Bandelets

Antonio Ortega, University of Southern CaliforniaTitle: Application-specific lossy signal compression for distributed signal processing

P. Oswald, Bell Labs, Lucent TechnologiesTitle: Smoothness of nonlinear subdivision based on median interpolation

Justin K. Romberg, Michael B. Wakin, Hyeokho Choi, Richard G. Baraniuk, Dept. of Electrical and Computer Engineering Rice UniversityTitle: Geometric Modeling of Edges in Images

Ivan Selesnick and Levent Sendur, Electrical and Computer Engineering, Polytechnic UniversityTitle: Bivariate Probability Models and Shrinkage Functions

Emina Soljanin, Bell Labs, Lucent

Gilbert Strang and Per-Olof Persson, MITTitle: Filtering and Signal Processing

Martin Vetterli, Ecole Polytechnique Federale de Lausanne and University of California, BerkeleyTitle: Sampling Signals with Finite Rate of Innovation