On the Performance of Turbo Signal Recovery with Partial DFT Sensing Matrices

TL;DR

This paper analyzes the turbo signal recovery algorithm's performance with partial DFT matrices in compressed sensing, demonstrating it surpasses the approximate message passing algorithm with IID sensing matrices through state evolution analysis.

Contribution

It provides a theoretical performance comparison showing TSR with partial DFT matrices outperforms AMP with IID matrices, supported by state evolution analysis.

Findings

TSR with partial DFT matrices outperforms AMP with IID matrices

State evolution analysis confirms the superiority of TSR in this setting

Theoretical proof of performance advantage

Abstract

This letter is on the performance of the turbo signal recovery (TSR) algorithm for partial discrete Fourier transform (DFT) matrices based compressed sensing. Based on state evolution analysis, we prove that TSR with a partial DFT sensing matrix outperforms the well-known approximate message passing (AMP) algorithm with an independent identically distributed (IID) sensing matrix.