Compressive Sensing and Structured Random Matrices

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

• Dokumententyp: Buchbeitrag
• Keywords: Compressive sensing; basis pursuit; structured random matrices; condition numbers; random partial Fourier matrix; partial random circulant matrix; Khintchineinequalities; bounded orthogonal systems
• Fakultät: Mathematik, Informatik und Statistik > Mathematik > Lehrstuhl für Mathematik der Informationsverarbeitung
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• ISBN: 978-3-11-022614-0
• Ort: Berlin ; New York, NY
• Sprache: Englisch