Modified-CS: Modifying Compressive Sensing for Problems with Partially Known Support

Details Modified-CS: Modifying Compressive Sensing for Problems with Partially Known Support Modified-CS: Modifying Compressive Sensing for Problems with Partially Known Support

2009-03-30

arxiv.org/abs/0903.5066v5

IEEE Trans. Signal Processing, pages 4595--4607, vol. 58 (9), September 2010

Computer Science

Information Theory

To Appear in IEEE Trans. Signal Processing, September 2010, shorter version presented at ISIT 2009

Scientific paper

10.1109/TSP.2010.2051150

We study the problem of reconstructing a sparse signal from a limited number of its linear projections when a part of its support is known, although the known part may contain some errors. The ``known" part of the support, denoted T, may be available from prior knowledge. Alternatively, in a problem of recursively reconstructing time sequences of sparse spatial signals, one may use 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 relaxation of the following problem: find the signal that satisfies the data constraint and is sparsest outside of T. We obtain sufficient conditions for exact reconstruction using modified-CS. These are much weaker than those needed for compressive sensing (CS) when the sizes of the unknown part of the support and of errors in the known part are small compared to the support size. An important extension called Regularized Modified-CS (RegModCS) is developed which also uses prior signal estimate knowledge. Simulation comparisons for both sparse and compressible signals are shown.

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