Advances in Sparse Signal Representation

Organizers: Mujdat Cetin (Massachusetts Institute of Technology) and Jean-Jacques Fuchs (IRISA)

Representing data in the most parsimonious terms is at the core of many signal processing applications, involving, e.g. signal analysis, compression, or estimation. While it is customary (e.g. in tasks such as signal analysis) to use models imposing sparsity in a transform domain such as the Fourier or wavelet domain, it is more natural to think of signals as composed of more diverse phenomena than what can be captured by a single transform. Furthermore, such phenomena emerge naturally through the structure of many problems, hence they could, in principle, be exploited. These realizations open up the area of sparse signal representation using general collections of generating elements. Such representations would be of interest in a wide range of applications. However finding these sparse representations in an optimal fashion is a challenging task, and has remained an unchartered territory until recently. In the last few years, we have witnessed very important progress in this area, leading to rigorous results showing that optimally sparse representations can be found by efficient techniques in certain cases. These results not only have immediate direct implications for signal processing applications, but also inspire a wide range of further questions. As a result, there is currently much research activity in both theoretical and practical aspects of sparse signal representation. This special session aims to provide a coherent picture of recent advances in sparse signal representation, the current state, and existing challenges.

Overview lecture:
  Title: Recent Advances in Sparsity-Driven Signal Recovery
  Author: D. L. Donoho, Y. Tsaig (Stanford University)

Regular lectures:

• Title: A Simple Test to Check the Optimality of Sparse Signal Approximations
  Authors: R. Gribonval (IRISA), R. M. Figueras i Ventura, and P. Vandergheynst (EPFL)
• Title: Simultaneous Sparse Approximation via Greedy Pursuit
  Authors: J. A. Tropp, A. C. Gilbert, and M. J. Strauss (Univ. of Michigan)
• Title: Reduced Complexity Bounded Error Subset Selection
  Authors: M. Alghoniemy (Univ. of Alexandria) and A. H. Tewfik (Univ. of Minnesota)
• Title: Sparsity and Uniqueness for Some Specific Under-determined Linear Systems
  Author: J.-J. Fuchs (IRISA)
• Title: Homotopy Continuation for Sparse Signal Representation
  Authors: D. M. Malioutov, M. Cetin, and A. S. Willsky (MIT)