Worst configurations (instantons) for compressed sensing over reals: a channel coding approach
- Los Alamos National Laboratory
- UNIV OF AZ
We consider Linear Programming (LP) solution of a Compressed Sensing (CS) problem over reals, also known as the Basis Pursuit (BasP) algorithm. The BasP allows interpretation as a channel-coding problem, and it guarantees the error-free reconstruction over reals for properly chosen measurement matrix and sufficiently sparse error vectors. In this manuscript, we examine how the BasP performs on a given measurement matrix and develop a technique to discover sparse vectors for which the BasP fails. The resulting algorithm is a generalization of our previous results on finding the most probable error-patterns, so called instantons, degrading performance of a finite size Low-Density Parity-Check (LDPC) code in the error-floor regime. The BasP fails when its output is different from the actual error-pattern. We design CS-Instanton Search Algorithm (ISA) generating a sparse vector, called CS-instanton, such that the BasP fails on the instanton, while its action on any modification of the CS-instanton decreasing a properly defined norm is successful. We also prove that, given a sufficiently dense random input for the error-vector, the CS-ISA converges to an instanton in a small finite number of steps. Performance of the CS-ISA is tested on example of a randomly generated 512 * 120 matrix, that outputs the shortest instanton (error vector) pattern of length 11.
- Research Organization:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- AC52-06NA25396
- OSTI ID:
- 983922
- Report Number(s):
- LA-UR-10-00281; LA-UR-10-281; TRN: US1005200
- Country of Publication:
- United States
- Language:
- English
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