Compressed Sensing for Block-Sparse Smooth Signals

TL;DR

This paper introduces novel reconstruction algorithms for smooth, block-sparse signals from compressed measurements, utilizing group-sparse regularizations and fusion to enhance signal recovery with low-complexity solvers.

Contribution

It proposes new algorithms combining group-sparse LASSO and fusion techniques, addressing varying group sizes and smoothness in block-sparse signal reconstruction.

Findings

Effective reconstruction of smooth block-sparse signals from compressed data.

Low-complexity algorithms based on ADMM for practical implementation.

Improved handling of varying group sizes in signal recovery.

Abstract

We present reconstruction algorithms for smooth signals with block sparsity from their compressed measurements. We tackle the issue of varying group size via group-sparse least absolute shrinkage selection operator (LASSO) as well as via latent group LASSO regularizations. We achieve smoothness in the signal via fusion. We develop low-complexity solvers for our proposed formulations through the alternating direction method of multipliers.