An M* Proxy for Sparse Recovery Performance

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.