Using Sparse Principal Component Methods for Approximating Restricted Isometry Constants of Complex-Valued Tight Frames

Abstract

For the estimation of constants in the standard restricted isometry condition for a complex-valued tight frame, a generalization of techniques related to Sparse Principal Component Analysis is developed and applied. We consider certain optimization reformulations of the problem and iterative algorithms for approximating sparse solutions. The eciency of methods is veried by numerical results obtained for several important test examples of tight frames.