On sparsity averaging

TL;DR

The paper reviews and extends the SARA method, demonstrating its superior performance in compressed sensing image reconstruction over single-frame sparsity methods, especially in radio astronomy applications.

Contribution

It extends the SARA algorithm and provides simulation results showing its advantages over traditional single-frame sparsity regularization methods.

Findings

SARA outperforms single-frame sparsity methods in image reconstruction.

SARA shows significant improvements in spread spectrum and Fourier acquisition scenarios.

The method is particularly effective in radio astronomy imaging.

Abstract

Recent developments in Carrillo et al. (2012) and Carrillo et al. (2013) introduced a novel regularization method for compressive imaging in the context of compressed sensing with coherent redundant dictionaries. The approach relies on the observation that natural images exhibit strong average sparsity over multiple coherent frames. The associated reconstruction algorithm, based on an analysis prior and a reweighted $\ell_1$ scheme, is dubbed Sparsity Averaging Reweighted Analysis (SARA). We review these advances and extend associated simulations establishing the superiority of SARA to regularization methods based on sparsity in a single frame, for a generic spread spectrum acquisition and for a Fourier acquisition of particular interest in radio astronomy.