Sparsity Averaging for Compressive Imaging

TL;DR

This paper introduces a new sparsity prior for compressive imaging that leverages the average sparsity of natural images across multiple coherent frames, improving reconstruction quality.

Contribution

It proposes a novel average sparsity prior and an analysis reweighted  algorithm, demonstrating superior performance over existing sparsity-promoting methods.

Findings

Average sparsity outperforms single basis sparsity priors.

The proposed method improves reconstruction quality in compressive imaging.

Extensive simulations validate the effectiveness of the new prior.

Abstract

We discuss a novel sparsity prior for compressive imaging in the context of the theory of compressed sensing with coherent redundant dictionaries, based on the observation that natural images exhibit strong average sparsity over multiple coherent frames. We test our prior and the associated algorithm, based on an analysis reweighted $\ell_1$ formulation, through extensive numerical simulations on natural images for spread spectrum and random Gaussian acquisition schemes. Our results show that average sparsity outperforms state-of-the-art priors that promote sparsity in a single orthonormal basis or redundant frame, or that promote gradient sparsity. Code and test data are available at https://github.com/basp-group/sopt.