Recovery of sparse perturbations in Least Squares problems
Author
Pilanci, M.
Arıkan, Orhan
Date
2011Source Title
2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
Print ISSN
1520-6149
Publisher
IEEE
Pages
3912 - 3915
Language
English
Type
Conference PaperItem Usage Stats
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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.
Keywords
Compressed SensingMatrix 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