D-OAMP: A Denoising-based Signal Recovery Algorithm for Compressed Sensing

TL;DR

This paper introduces D-OAMP, an extension of orthogonal AMP that integrates generic denoisers for improved signal recovery in compressed sensing, demonstrating better performance than D-AMP especially with partial orthogonal matrices.

Contribution

The paper develops D-OAMP, a novel algorithm that combines OAMP with generic denoisers, expanding its applicability and improving recovery performance in compressed sensing.

Findings

D-OAMP's performance aligns well with state evolution predictions.

D-OAMP outperforms D-AMP in convergence speed.

D-OAMP achieves higher recovery accuracy with partial orthogonal matrices.

Abstract

Approximate message passing (AMP) is an efficient iterative signal recovery algorithm for compressed sensing (CS). For sensing matrices with independent and identically distributed (i.i.d.) Gaussian entries, the behavior of AMP can be asymptotically described by a scaler recursion called state evolution. Orthogonal AMP (OAMP) is a variant of AMP that imposes a divergence-free constraint on the denoiser. In this paper, we extend OAMP to incorporate generic denoisers, hence the name D-OAMP. Our numerical results show that state evolution predicts the performance of D-OAMP well for generic denoisers when i.i.d. Gaussian or partial orthogonal sensing matrices are involved. We compare the performances of denosing-AMP (D-AMP) and D-OAMP for recovering natural images from CS measurements. Simulation results show that D-OAMP outperforms D-AMP in both convergence speed and recovery accuracy for partial orthogonal sensing matrices.