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Full-Text Articles in Physical Sciences and Mathematics
The Road To Deterministic Matrices With The Restricted Isometry Property, Afonso S. Bandeira, Matthew C. Fickus, Dustin G. Mixon, Percy Wong
The Road To Deterministic Matrices With The Restricted Isometry Property, Afonso S. Bandeira, Matthew C. Fickus, Dustin G. Mixon, Percy Wong
Faculty Publications
The restricted isometry property (RIP) is a well-known matrix condition that provides state-of-the-art reconstruction guarantees for compressed sensing. While random matrices are known to satisfy this property with high probability, deterministic constructions have found less success. In this paper, we consider various techniques for demonstrating RIP deterministically, some popular and some novel, and we evaluate their performance. In evaluating some techniques, we apply random matrix theory and inadvertently find a simple alternative proof that certain random matrices are RIP. Later, we propose a particular class of matrices as candidates for being RIP, namely, equiangular tight frames (ETFs). Using the known …