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

Igor Kaporin | Zendy

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

Author(s) -

Igor Kaporin

Publication year - 2019

Publication title -

destech transactions on computer science and engineering

Language(s) - English

Resource type - Journals

ISSN - 2475-8841

DOI - 10.12783/dtcse/optim2018/27941

Subject(s) - isometry (riemannian geometry) , generalization , mathematics , frame (networking) , principal component analysis , sparse approximation , component (thermodynamics) , algorithm , restricted isometry property , computer science , mathematical optimization , compressed sensing , mathematical analysis , statistics , physics , telecommunications , thermodynamics

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.

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