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Abstract: We study the problem of reconstructing a sparse signal from a limited numberof its linear projections when a part of its support is known, although theknown part may contain some errors. The ``known- part of the support, denotedT, may be available from prior knowledge. Alternatively, in a problem ofrecursively reconstructing time sequences of sparse spatial signals, one mayuse the support estimate from the previous time instant as the ``known- part.The idea of our proposed solution modified-CS is to solve a convex relaxationof the following problem: find the signal that satisfies the data constraintand is sparsest outside of T. We obtain sufficient conditions for exactreconstruction using modified-CS. These are much weaker than those needed forcompressive sensing CS when the sizes of the unknown part of the support andof errors in the known part are small compared to the support size. Animportant extension called Regularized Modified-CS RegModCS is developedwhich also uses prior signal estimate knowledge. Simulation comparisons forboth sparse and compressible signals are shown.



Author: Namrata Vaswani, Wei Lu

Source: https://arxiv.org/



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