Article
Structured least squares with bounded data uncertainties
Proceedings  ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing 01/2009; DOI: 10.1109/ICASSP.2009.4960320
Source: DBLP

Conference Paper: Recovery of sparse perturbations in Least Squares problems.
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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 � 0/� 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.Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2011, May 2227, 2011, Prague Congress Center, Prague, Czech Republic; 01/2011  [Show abstract] [Hide abstract]
ABSTRACT: A novel approach is proposed to provide robust and accurate estimates for linear regression problems when both the measurement vector and the coefficient matrix are structured and subject to errors or uncertainty. A new analytic formulation is developed in terms of the gradient flow of the residual norm to analyze and provide estimates to the regression. The presented analysis enables us to establish theoretical performance guarantees to compare with existing methods and also offers a criterion to choose the regularization parameter autonomously. Theoretical results and simulations in applications such as blind identification, multiple frequency estimation and deconvolution show that the proposed technique outperforms alternative methods in meansquared error for a significant range of signaltonoise ratio values.IEEE Transactions on Signal Processing 06/2010; · 3.20 Impact Factor
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