Compressive Sensing and Structured Random Matrices

Rauhut, Holger (2010): Compressive Sensing and Structured Random Matrices. In: Fornasier, Massimo (ed.) : Theoretical Foundations and Numerical Methods for Sparse Recovery. Radon Series on Computational and Applied Mathematics, Vol. 9. Berlin ; New York, NY: De Gruyter. pp. 1-92

Abstract

These notes give a mathematical introduction to compressive sensing focusingon recovery using`1-minimization and structured random matrices. An emphasis is put ontechniques for proving probabilistic estimates for condition numbers of structured random ma-trices. Estimates of this type are key to providing conditions that ensure exact or approximaterecovery of sparse vectors using`1-minimization.

• Item Type: Book Section
• Keywords: Compressive sensing; basis pursuit; structured random matrices; condition numbers; random partial Fourier matrix; partial random circulant matrix; Khintchineinequalities; bounded orthogonal systems
• Faculties: Mathematics, Computer Science and Statistics > Mathematics > Chair of Mathematics of Information Processing
• Subjects: 500 Science > 510 Mathematics
• ISBN: 978-3-11-022614-0
• Place of Publication: Berlin ; New York, NY
• Language: English