ISPSeminar

## (**Invited talk**)

**Title**: "Greedy algorithms for multi-channel sparse recovery"

**Speaker**: Jean-François Determe (ULB & UCL, Belgium)

**Location**: "Shannon" Seminar Room (a105)
Place du Levant 3, Maxwell Building, 1st floor

**Date / Time (duration)**: Wednesday 10/01/2018, 11h00 (~ 45')

(slides)

**Abstract**:

Research on “compressive sensing” (CS) has shown that it is possible to retrieve high-dimensional signals using a limited set of (often random) linear measurements. For CS to work properly, the signal to be retrieved must be sparse, which means that most of its components (e.g., 90 % of them) are zero. Many algorithms relying on CS can reliably recover sparse signals on the basis of a number of measurements that essentially scales with sparsity level (instead of scaling with the number of dimensions).

This talk focuses on the simultaneous retrieval of several sparse signals sharing a common structure, which stems from the indices of their non-zero entries being similar. Such sets of sparse signals (and the corresponding sets of measurements) typically correspond to systems that comprise several sensors measuring a unique phenomenon at different time instants and locations; the structure of the phenomenon does not depend on a location or time instant but local effects and limited variations over time may nevertheless generate different measurement vectors.
Simultaneous retrieval is typically more reliable than other approaches that process the measurements of all the sparse signals in a more independent way. This talk studies a particular algorithm that performs simultaneous retrieval, namely simultaneous orthogonal matching pursuit (SOMP).

First of all, we shall discuss the reliability of SOMP in the noiseless case. On the basis of those first results, we shall investigate the noise robustness of SOMP, which amounts to quantifying to what extent adding noise to the measurements decreases the reliability of SOMP. Finally, we shall also briefly describe a noise stabilization procedure for SOMP. The procedure weights the impact on SOMP of all the measurement vectors according to their respective signal-to-noise ratios (SNRs); thereby, high-SNR measurement vectors become more prominent than their low-SNR counterparts.