Compressed Sensing With Side Information: Geometrical Interpretation and Performance Bounds

TL;DR

This paper analyzes compressed sensing with side information, showing how different minimization methods affect measurement requirements and providing geometric insights and bounds for successful signal reconstruction.

Contribution

It introduces a geometric interpretation and bounds for compressed sensing with side information, comparing L1-L1 and L1-L2 minimization effectiveness.

Findings

L1-L1 minimization reduces measurements with good side info

L1-L2 minimization less effective in measurement reduction

Geometrical insights explain performance differences

Abstract

We address the problem of Compressed Sensing (CS) with side information. Namely, when reconstructing a target CS signal, we assume access to a similar signal. This additional knowledge, the side information, is integrated into CS via L1-L1 and L1-L2 minimization. We then provide lower bounds on the number of measurements that these problems require for successful reconstruction of the target signal. If the side information has good quality, the number of measurements is significantly reduced via L1-L1 minimization, but not so much via L1-L2 minimization. We provide geometrical interpretations and experimental results illustrating our findings.