Handbook of Blind Source Separation

Chapter 10

Sparse component analysis

R. Gribonval and M. Zibulevsky

10.1 Introduction

Sparse decomposition techniques for signals and images underwent considerable development during the flourishing of wavelet-based compression and denoising methods [75] in the early 1990s. Some ten years elapsed before these techniques began to be fully exploited for blind source separation [72,106,66,70,116,61,15,111]. Their main impact is that they provide a relatively simple framework for separating a number of sources exceeding the number of observed mixtures. Also they greatly improve quality of separation in the case of square mixing matrix.

The underlying assumption is essentially geometrical [98], differing considerably from the traditional assumption of ...