The bulk of the Compressive sensing (CS) literature has focused on the case where the acquired signal has a sparse or compressible representation in an orthonormal basis. In practice, however, there are many signals that cannot be sparsely represented or approximated using an orthonormal basis, but that do have sparse representations in a redundant dictionary. Standard results in CS can sometimes be extended to handle this case provided that the dictionary is sufficiently incoherent or well-conditioned, but these approaches fail to address the case of a truly redundant or overcomplete dictionary.

This software package implements a variant of the iterative reconstruction algorithm CoSaMP for this more challenging setting. In contrast to prior approaches, the method is "signal-focused"; that is, it is oriented around recovering the signal rather than its dictionary coefficients.

For further details, see the paper "Signal Space CoSaMP for Sparse Recovery with Redundant Dictionaries," by M.A. Davenport, D. Needell, and M.B. Wakin.

Signal Space CoSaMP can be downloaded here; the Matlab files entitled "demo_*.m" provide several examples of how to invoke Signal Space CoSaMP and compare the results to traditional CS algorithms. The Matlab data (.mat) files necessary to reproduce the figures presented in the paper can be downloaded here. Please e-mail mdav-at-gatech-dot-edu if you find any bugs or have any questions.