Simultaneous Sparse Approximation and Common Component Extraction using Fast Distributed Compressive Sensing

TL;DR

This paper introduces a hierarchical algorithm for distributed compressive sensing that efficiently recovers multiple correlated signals, demonstrated on video background extraction, reducing memory and computational demands.

Contribution

A novel hierarchical algorithm for joint sparse recovery in distributed compressive sensing, improving efficiency for large-scale signal sets.

Findings

Enhanced recovery efficiency for multiple signals

Reduced memory and computational requirements

Effective application to video background extraction

Abstract

Simultaneous sparse approximation is a generalization of the standard sparse approximation, for simultaneously representing a set of signals using a common sparsity model. Generalizing the compressive sensing concept to the simultaneous sparse approximation yields distributed compressive sensing (DCS). DCS finds the sparse representation of multiple correlated signals using the common + innovation signal model. However, DCS is not efficient for joint recovery of a large number of signals since it requires large memory and computational time. In this paper, we propose a new hierarchical algorithm to implement the jointly sparse recovery framework of DCS more efficiently. The proposed algorithm is applied to video background extraction problem, where the background corresponds to the common sparse activity across frames.