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An upper bound on the estimation error of the sparsest solution of underdetermined linear systems
Abstract : Let A be an n X m matrix with m > n, and suppose the underdetermined linear system As = x admits a unique sparse solution s0 (i.e. it has a solution s0 for which ks0k0 < 1 2 spark(A)). Suppose that we have somehow a solution (sparse or non-sparse) ^s of this system as an estimation of the true sparsest solution s0. Is it possible to construct an upper bound on the estimation error k^s - s0k2 without knowing s0? The answer is positive, and in this paper we construct such a bound which, in the case A has Unique Representation Property (URP), depends on the smallest singular value of all n X n submatrices of A.
Cited literature [30 references]
https://hal.inria.fr/inria-00369545
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Submitted on : Friday, March 20, 2009 - 11:42:09 AM
Last modification on : Tuesday, October 19, 2021 - 11:22:27 PM
Long-term archiving on: : Thursday, June 10, 2010 - 5:37:17 PM
Contributor : Ist Rennes Connect in order to contact the contributor
Submitted on : Friday, March 20, 2009 - 11:42:09 AM
Last modification on : Tuesday, October 19, 2021 - 11:22:27 PM
Long-term archiving on: : Thursday, June 10, 2010 - 5:37:17 PM
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