Modeling Sparse Deviations for Compressed Sensing using Generative Models

TL;DR

This paper introduces Sparse-Gen, a novel compressed sensing framework that combines generative models with sparse deviations, enabling accurate signal reconstruction over the full space and improving over existing methods.

Contribution

Sparse-Gen extends generative model-based compressed sensing by allowing sparse deviations, broadening the class of signals that can be accurately reconstructed.

Findings

Consistent improvements in reconstruction accuracy over competing methods.

Effective in transfer compressed sensing scenarios with limited target domain data.

Reduces classic sparse recovery to a special case, avoiding restrictive support assumptions.

Abstract

In compressed sensing, a small number of linear measurements can be used to reconstruct an unknown signal. Existing approaches leverage assumptions on the structure of these signals, such as sparsity or the availability of a generative model. A domain-specific generative model can provide a stronger prior and thus allow for recovery with far fewer measurements. However, unlike sparsity-based approaches, existing methods based on generative models guarantee exact recovery only over their support, which is typically only a small subset of the space on which the signals are defined. We propose Sparse-Gen, a framework that allows for sparse deviations from the support set, thereby achieving the best of both worlds by using a domain specific prior and allowing reconstruction over the full space of signals. Theoretically, our framework provides a new class of signals that can be acquired using compressed sensing, reducing classic sparse vector recovery to a special case and avoiding the restrictive support due to a generative model prior. Empirically, we observe consistent improvements in reconstruction accuracy over competing approaches, especially in the more practical setting of transfer compressed sensing where a generative model for a data-rich, source domain aids sensing on a data-scarce, target domain.