Turbo Compressed Sensing with Partial DFT Sensing Matrix

TL;DR

This paper introduces a turbo compressed sensing algorithm tailored for partial DFT sensing matrices, demonstrating superior performance over AMP and aligning with theoretical state evolution predictions.

Contribution

The paper presents a novel turbo compressed sensing algorithm specifically designed for partial DFT matrices, with validated state evolution and improved performance.

Findings

The algorithm outperforms AMP with partial DFT matrices.

State evolution matches replica method predictions.

Numerical results confirm the effectiveness of the proposed method.

Abstract

In this letter, we propose a turbo compressed sensing algorithm with partial discrete Fourier transform (DFT) sensing matrices. Interestingly, the state evolution of the proposed algorithm is shown to be consistent with that derived using the replica method. Numerical results demonstrate that the proposed algorithm outperforms the well-known approximate message passing (AMP) algorithm when a partial DFT sensing matrix is involved.