Iterative and greedy algorithms for the sparsity in levels model in compressed sensing

TL;DR

This paper introduces generalized iterative and greedy algorithms tailored for the sparsity in levels model in compressed sensing, demonstrating improved performance over unstructured methods in structured signal approximation tasks.

Contribution

It presents novel algorithms that promote structured sparsity in levels, outperforming traditional unstructured algorithms in numerical experiments.

Findings

Structured algorithms outperform unstructured variants in sparse in levels signals

Structure-promoting decoders excel in piecewise smooth function approximation

Numerical results confirm the effectiveness of the proposed methods

Abstract

Motivated by the question of optimal functional approximation via compressed sensing, we propose generalizations of the Iterative Hard Thresholding and the Compressive Sampling Matching Pursuit algorithms able to promote sparse in levels signals. We show, by means of numerical experiments, that the proposed algorithms are successfully able to outperform their unstructured variants when the signal exhibits the sparsity structure of interest. Moreover, in the context of piecewise smooth function approximation, we numerically demonstrate that the structure promoting decoders outperform their unstructured variants and the basis pursuit program when the encoder is structure agnostic.