Computing performance guarantees for compressed sensing

Author

Lee, Kiryung ; Bresler, Yoram

Author_Institution

Dept. of ECE, Univ. of Illinois-Urbana-Champaign, Urbana, IL

fYear

2008

fDate

March 31 2008-April 4 2008

Firstpage

5129

Lastpage

5132

Abstract

There are various conditions on the CS matrix for unique and stable recovery. These include universality, or spark, and UUP. Furthermore, quantitative bounds on the stability depend on related properties of the CS matrix. The construction of good CS matrices - satisfying the various properties - is key to successful practical applications of compressive sensing. Unfortunately, verifying the satisfiability of any of these properties for a given CS matrix involves infeasible combinatorial search. Our methods use i and semidefinite relaxation into a convex problem. Given a set of candidate CS matrices, our approach provides tools for the selection of good CS matrices with verified and quantitatively favorable performance.

Keywords

computability; matrix algebra; sampling methods; signal processing; combinatorial search; compressed sensing; compressive sampling matrix; satisfiability; Compressed sensing; Inverse problems; Polynomials; Prototypes; Random number generation; Sampling methods; Sparks; Sparse matrices; Stability; Uncertainty; Basis Pursuit; Compressive Sampling; Semidefinite Programming; Spark; Uniform Uncertainty Principle;

fLanguage

English

Publisher

ieee

Conference_Titel

Acoustics, Speech and Signal Processing, 2008. ICASSP 2008. IEEE International Conference on

Conference_Location

Las Vegas, NV

ISSN

1520-6149

Print_ISBN

978-1-4244-1483-3

Electronic_ISBN

1520-6149

Type

conf

DOI

10.1109/ICASSP.2008.4518813

Filename

4518813