Tutorial 13: Sparse Signal Recovery: Theory, Applications and Algorithms

Presented by

Bhaskar D. Rao, David P. Wipf

Abstract

Sparsity has emerged as a new and important concept in signal processing. A prototypical problem where sparsity is exploited is the sparse signal recovery problem. This tutorial examines theoretical and algorithmic issues that arise in sparse signal recovery problems. There are numerous signal processing applications where this problem naturally arises. Signal representation using overcomplete dictionaries, estimation of sparse communication channels with large delay spread, high resolution spectral analysis, brain imaging techniques such as MEG and EEG, are a few examples. More recently, the emergence of compressive sensing has generated considerable excitement and interest in this problem. This tutorial will examine the general problem of sparse signal recovery and the challenges associated with it. We will discuss potential applications and algorithms such as matching pursuit, basis pursuit, sparse Bayesian learning among others for solving the associated inverse problem. Lastly, we will examine the compressive sensing framework and the theoretical issues concerning the design of the sensing matrix and the underlying sparse recovery problem.

Intended Audience

This tutorial is suited for any individual with a background in digital signal processing. Signal processing researchers/engineers can benefit significantly by having at their disposal a variety of processing tools so that they can employ the appropriate tools for the various problems they encounter. We believe that the underlying principles covered in this tutorial have general applicability, and a comprehensive solution to the sparse recovery problem can have significant impact, providing new and valuable tools to the signal processing researcher/engineer.