2018/01/19 by Zhiyong Zhou, Jun Yu, Zhou, Zhiyong +1 · 1 citation
Computer Science · Engineering · Mathematics · Medicine · #Advanced MRI Techniques and Applications #Algorithm #Applied mathematics #Basis (linear algebra) #Basis pursuit #Bounded function #Compressed sensing #Computer science #Constant (computer programming) #Estimator #FOS: Computer and information sciences #Geometry #Information Theory (cs.IT) #Isotropy #Lasso (programming language) #Mathematical analysis #Mathematics #Microwave Imaging and Scattering Analysis #Singular value #Sparse and Compressive Sensing Techniques #Statistics #Verifiable secret sharing #cs.IT #math.IT
paper · pdf · doi:10.48550/arxiv.1801.06358
published in arXiv (Cornell University) (Cornell University)
arxiv created 2018/01/19 · openalex publication_date 2018/01/19 · arxiv updated 2018/01/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.