2008/03/05 by Florian M. Sebert, Florian Sebert, Leslie Ying +4
Computer Science · Engineering · Mathematics · #94A08 #94A20 #Blind Source Separation Techniques #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Mathematical Analysis and Transform Methods #Probability (math.PR) #Sparse and Compressive Sensing Techniques #cs.IT #math.IT #math.PR #msc:94A08 #msc:94A20
paper · pdf · doi:10.48550/arxiv.0803.0755
Preprint 16 pages, 1 figure
arxiv created 2008/03/05 · openalex publication_date 2008/03/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Recent work in compressed sensing theory shows that n× N independent and identically distributed (IID) sensing matrices whose entries are drawn independently from certain probability distributions guarantee exact recovery of a sparse signal with high probability even if n≪ N. Motivated by signal processing applications, random filtering with Toeplitz sensing matrices whose elements are drawn from the same distributions were considered and shown to also be sufficient to recover a sparse signal from reduced samples exactly with high probability. This paper considers Toeplitz block matrices as sensing matrices. They naturally arise in multichannel and multidimensional filtering applications and include Toeplitz matrices as special cases. It is shown that the probability of exact reconstruction is also high. Their performance is validated using simulations.