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In this work, we study the problem of reconstructing a sparse signal from alimited number of linear 'incoherent' noisy measurements, when a part of itssupport is known. The known part of the support may be available from priorknowledge or from the previous time instant (in applications requiringrecursive reconstruction of a time sequence of sparse signals, e.g. dynamicMRI). We study a modification of Basis Pursuit Denoising (BPDN) and bound itsreconstruction error. A key feature of our work is that the bounds that weobtain are computable. Hence, we are able to use Monte Carlo to study theiraverage behavior as the size of the unknown support increases. We alsodemonstrate that when the unknown support size is small, modified-BPDN boundsare much tighter than those for BPDN, and hold under much weaker sufficientconditions (require fewer measurements).

Modified Basis Pursuit Denoising(MODIFIED-BPDN) for Noisy Compressive Sensing with Partially Known Support