Signal Recovery under Cumulative Coherence

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.

References in corpus (7)

• Simultaneous analysis of Lasso and Dantzig selector
• Fast and Efficient Compressive Sensing using Structurally Random Matrices
• The Dantzig selector: Statistical estimation when $p$ is much larger than $n$
• Smoothing and Decomposition for Analysis Sparse Recovery
• Compressed Sensing and Affine Rank Minimization under Restricted Isometry
• One condition for solution uniqueness and robustness of both l1-synthesis and l1-analysis minimizations
• Sparse approximation property and stable recovery of sparse signals from noisy measurements

Cited by in corpus (1)

• Deterministic Analysis of Weighted BPDN With Partially Known Support Information