Edinburgh Research Explorer

IMPROVED BOUNDS ON RESTRICTED ISOMETRY CONSTANTS FOR GAUSSIAN MATRICES

Research output: Contribution to journalArticle

Related Edinburgh Organisations

Open Access permissions

Open

Documents

Original languageEnglish
Pages (from-to)2882-2898
Number of pages17
JournalSIAM Journal on Matrix Analysis and Applications
Volume31
Issue number5
DOIs
Publication statusPublished - 2010

Abstract

The restricted isometry constant ( RIC) of a matrix A measures how close to an isometry is the action of A on vectors with few nonzero entries, measured in the l(2) norm. Specifically, the upper and lower RICs of a matrix A of size nxN are the maximum and the minimum deviation from unity (one) of the largest and smallest, respectively, square of singular values of all ((N)(k)) matrices formed by taking k columns from A. Calculation of the RIC is intractable for most matrices due to its combinatorial nature; however, many random matrices typically have bounded RIC in some range of problem sizes (k, n, N). We provide the best known bound on the RIC for Gaussian matrices, which is also the smallest known bound on the RIC for any large rectangular matrix. Our results are built on the prior bounds of Blanchard, Cartis, and Tanner [SIAM Rev., to appear], with improvements achieved by grouping submatrices that share a substantial number of columns.

    Research areas

  • Wishart matrices, compressed sensing, sparse approximation, restricted isometry constant, phase transitions, Gaussian matrices, singular values of random matrices, PRINCIPAL COMPONENT ANALYSIS, SIGNAL RECONSTRUCTION

Download statistics

No data available

ID: 582441