QCM-SGM+: Improved Quantized Compressed Sensing With Score-Based Generative Models

TL;DR

This paper introduces QCS-SGM+, an advanced algorithm for quantized compressed sensing that leverages score-based generative models and Bayesian inference to handle general sensing matrices, significantly improving recovery performance over previous methods.

Contribution

QCS-SGM+ extends the original QCS-SGM to work with arbitrary sensing matrices using expectation propagation, enhancing practical applicability and performance.

Findings

QCS-SGM+ outperforms QCS-SGM on general sensing matrices.

The method effectively handles extreme quantization like 1-bit measurements.

Extensive experiments validate the superiority of QCS-SGM+.

Abstract

In practical compressed sensing (CS), the obtained measurements typically necessitate quantization to a limited number of bits prior to transmission or storage. This nonlinear quantization process poses significant recovery challenges, particularly with extreme coarse quantization such as 1-bit. Recently, an efficient algorithm called QCS-SGM was proposed for quantized CS (QCS) which utilizes score-based generative models (SGM) as an implicit prior. Due to the adeptness of SGM in capturing the intricate structures of natural signals, QCS-SGM substantially outperforms previous QCS methods. However, QCS-SGM is constrained to (approximately) row-orthogonal sensing matrices as the computation of the likelihood score becomes intractable otherwise. To address this limitation, we introduce an advanced variant of QCS-SGM, termed QCS-SGM+, capable of handling general matrices effectively. The key idea is a Bayesian inference perspective on the likelihood score computation, wherein expectation propagation is employed for its approximate computation. Extensive experiments are conducted, demonstrating the substantial superiority of QCS-SGM+ over QCS-SGM for general sensing matrices beyond mere row-orthogonality.