Compressive Imaging via Approximate Message Passing with Image Denoising

TL;DR

This paper introduces AMP-based compressive imaging algorithms using wavelet denoisers, significantly improving runtime and, in the case of AMP-Wiener, reconstruction quality over existing methods.

Contribution

It presents novel AMP algorithms with wavelet denoisers for compressive imaging, enhancing speed and accuracy compared to prior approaches.

Findings

AMP-Wiener achieves lower MSE than existing algorithms.

Both AMP-ABE and AMP-Wiener run faster than current methods.

AMP-Wiener outperforms in reconstruction quality.

Abstract

We consider compressive imaging problems, where images are reconstructed from a reduced number of linear measurements. Our objective is to improve over existing compressive imaging algorithms in terms of both reconstruction error and runtime. To pursue our objective, we propose compressive imaging algorithms that employ the approximate message passing (AMP) framework. AMP is an iterative signal reconstruction algorithm that performs scalar denoising at each iteration; in order for AMP to reconstruct the original input signal well, a good denoiser must be used. We apply two wavelet based image denoisers within AMP. The first denoiser is the "amplitude-scaleinvariant Bayes estimator" (ABE), and the second is an adaptive Wiener filter; we call our AMP based algorithms for compressive imaging AMP-ABE and AMP-Wiener. Numerical results show that both AMP-ABE and AMP-Wiener significantly improve over the state of the art in terms of runtime. In terms of reconstruction quality, AMP-Wiener offers lower mean square error (MSE) than existing compressive imaging algorithms. In contrast, AMP-ABE has higher MSE, because ABE does not denoise as well as the adaptive Wiener filter.