Theoretical Analysis of Compressive Sensing via Random Filter

TL;DR

This paper provides a theoretical analysis of compressive sensing using random filters, demonstrating that signals sparse in any basis can be accurately recovered with a universal measurement strategy involving convolution and subsampling.

Contribution

The paper generalizes and refines previous work to establish a universal random filter-based measurement method for compressive sensing.

Findings

Exact recovery of S-sparse signals from Slogn measurements

Universal applicability to signals sparse in any basis

High probability of successful reconstruction

Abstract

In this paper, the theoretical analysis of compressive sensing via random filter, firstly outlined by J. Romberg [compressive sensing by random convolution, submitted to SIAM Journal on Imaging Science on July 9, 2008], has been refined or generalized to the design of general random filter used for compressive sensing. This universal CS measurement consists of two parts: one is from the convolution of unknown signal with a random waveform followed by random time-domain subsampling; the other is from the directly time-domain subsampling of the unknown signal. It has been shown that the proposed approach is a universally efficient data acquisition strategy, which means that the n-dimensional signal which is S sparse in any sparse representation can be exactly recovered from Slogn measurements with overwhelming probability.