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      • Department of Electrical and Electronics Engineering
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      Recovery of sparse perturbations in Least Squares problems

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      Author
      Pilanci, M.
      Arıkan, Orhan
      Date
      2011
      Source 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 Paper
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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 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
      Permalink
      http://hdl.handle.net/11693/28375
      Published Version (Please cite this version)
      http://dx.doi.org/10.1109/ICASSP.2011.5947207
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      • Department of Electrical and Electronics Engineering 3524
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