  In this work, we study the problem of reconstructing a sparse signal from a
limited number of linear 'incoherent' noisy measurements, when a part of its
support is known. The known part of the support may be available from prior
knowledge or from the previous time instant (in applications requiring
recursive reconstruction of a time sequence of sparse signals, e.g. dynamic
MRI). We study a modification of Basis Pursuit Denoising (BPDN) and bound its
reconstruction error. A key feature of our work is that the bounds that we
obtain are computable. Hence, we are able to use Monte Carlo to study their
average behavior as the size of the unknown support increases. We also
demonstrate that when the unknown support size is small, modified-BPDN bounds
are much tighter than those for BPDN, and hold under much weaker sufficient
conditions (require fewer measurements).
