Structural Sparsity in Multiple Measurements

TL;DR

This paper introduces a new structured sparsity model for distributed compressed sensing in MMV settings, enabling better reconstruction of complex sparse data in applications like seismic exploration.

Contribution

It extends row-sparsity to more general structured sparsity models and develops a novel LASSO-type functional with an effective projected gradient descent algorithm.

Findings

Effective reconstruction demonstrated on real data

New structured sparsity model generalizes previous approaches

Algorithm converges reliably in extensive simulations

Abstract

We propose a novel sparsity model for distributed compressed sensing in the multiple measurement vectors (MMV) setting. Our model extends the concept of row-sparsity to allow more general types of structured sparsity arising in a variety of applications like, e.g., seismic exploration and non-destructive testing. To reconstruct structured data from observed measurements, we derive a non-convex but well-conditioned LASSO-type functional. By exploiting the convex-concave geometry of the functional, we design a projected gradient descent algorithm and show its effectiveness in extensive numerical simulations, both on toy and real data.