Compressed Sensing via Measurement-Conditional Generative Models

TL;DR

This paper introduces a framework that enhances pre-trained generative models in compressed sensing by incorporating measurement data, leading to significantly improved signal reconstruction accuracy and relaxed recovery conditions.

Contribution

It proposes a simple, adaptable framework that allows measurement-conditional prior learning, improving existing compressed sensing methods with pre-trained generators.

Findings

Achieves up to tenfold reduction in reconstruction error.

Demonstrates superior performance across various experiments.

Theoretically relaxes signal presence conditions for recovery.

Abstract

A pre-trained generator has been frequently adopted in compressed sensing (CS) due to its ability to effectively estimate signals with the prior of NNs. In order to further refine the NN-based prior, we propose a framework that allows the generator to utilize additional information from a given measurement for prior learning, thereby yielding more accurate prediction for signals. As our framework has a simple form, it is easily applied to existing CS methods using pre-trained generators. We demonstrate through extensive experiments that our framework exhibits uniformly superior performances by large margin and can reduce the reconstruction error up to an order of magnitude for some applications. We also explain the experimental success in theory by showing that our framework can slightly relax the stringent signal presence condition, which is required to guarantee the success of signal recovery.