Sparse recovery based on q-ratio constrained minimal singular values

Abstract

We study verifiable sufficient conditions and computable performance bounds for sparse recovery algorithms such as the Basis Pursuit, the Dantzig selector and the Lasso estimator, in terms of a newly defined family of quality measures for the measurement matrices. With high probability, the developed measures for subgaussian random matrices are bounded away from zero as long as the number of measurements is reasonably large. Comparing to the restricted isotropic constant based performance analysis, the arguments in this paper are much more concise and the obtained bounds are tighter. Numerical experiments are presented to illustrate our theoretical results.

References in corpus (5)

• Simultaneous analysis of Lasso and Dantzig selector
• Performance Analysis of Sparse Recovery Based on Constrained Minimal Singular Values
• Estimation of block sparsity in compressive sensing
• On robust width property for Lasso and Dantzig selector
• Stable and robust ${\ell }_p$-constrained compressive sensing recovery via robust width property

Cited by in corpus (1)

• On $q$-ratio CMSV for sparse recovery