Recovery of sparse perturbations in Least Squares problems

Date
2011
Advisor
Instructor
Source Title
2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
Print ISSN
1520-6149
Electronic ISSN
Publisher
IEEE
Volume
Issue
Pages
3912 - 3915
Language
English
Type
Conference Paper
Journal Title
Journal ISSN
Volume Title
Abstract

We show that the exact recovery of sparse perturbations on the coefficient matrix in overdetermined Least Squares problems is possible for a large class of perturbation structures. The well established theory of Compressed Sensing enables us to prove that if the perturbation structure is sufficiently incoherent, then exact or stable recovery can be achieved using linear programming. We derive sufficiency conditions for both exact and stable recovery using known results of ℓ 0/ℓ 1 equivalence. However the problem turns out to be more complicated than the usual setting used in various sparse reconstruction problems. We propose and solve an optimization criterion and its convex relaxation to recover the perturbation and the solution to the Least Squares problem simultaneously. Then we demonstrate with numerical examples that the proposed method is able to recover the perturbation and the unknown exactly with high probability. The performance of the proposed technique is compared in blind identification of sparse multipath channels. © 2011 IEEE.

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Book Title
Keywords
Compressed Sensing, Matrix Identification, Sparse Multipath Channels, Structured Perturbations, Structured Total Least Squares, Compressed sensing, Matrix identification, Sparse multi-path channel, Structured perturbations, Structured total least squares, Communication channels (information theory), Least squares approximations, Multipath propagation, Numerical methods, Optimization, Relaxation processes, Signal reconstruction, Speech communication, Recovery
Citation
Published Version (Please cite this version)