Signal Recovery under Cumulative Coherence

TL;DR

This paper investigates signal recovery using cumulative coherence, demonstrating the equivalence of Lasso and Dantzig selector, and establishing the advantages of cumulative coherence for sparse signal recovery through theoretical analysis and numerical experiments.

Contribution

It establishes the relationship between Lasso and Dantzig selector under cumulative coherence and shows the benefits of cumulative coherence for sparse signal recovery.

Findings

Lasso and Dantzig selector behave similarly under cumulative coherence

Cumulative coherence implies the restricted eigenvalue condition

Numerical experiments show advantages for three matrix classes

Abstract

This paper considers signal recovery in the framework of cumulative coherence. First, we show that the Lasso estimator and the Dantzig selector exhibit similar behavior under the cumulative coherence. Then we estimate the approximation equivalence between the Lasso and the Dantzig selector by calculating prediction loss difference under the condition of cumulative coherence. And we also prove that the cumulative coherence implies the restricted eigenvalue condition. Last, we illustrate the advantages of cumulative coherence condition for three class matrices, in terms of the recovery performance of sparse signals via extensive numerical experiments.