An M* Proxy for Sparse Recovery Performance

TL;DR

This paper introduces a new lower bound for sparse recovery performance that acts as a proxy to improve dictionary learning and MRI sampling schemes, enhancing reconstruction quality.

Contribution

It proposes a novel tractable lower bound for sparse recovery thresholds, used to improve dictionary learning and MRI sampling design.

Findings

Improved dictionary learning with better generalization.

Enhanced MRI sampling schemes with higher reconstruction accuracy.

Validated proxy's effectiveness in practical applications.

Abstract

This paper provides a new tractable lower bound for the sparse recovery threshold of sensing matrices. This lower bound is used as a proxy to quantify the quality of sensing matrices in two different applications. First, it serves as regularization for the classical dictionary learning problem in order to learn dictionaries with better generalisation properties on unseen data. Then, the proxy is used to design sampling schemes for MRI acquisition that exhibit high reconstruction performances.