Sparse Representation in Redundant Systems

CSIC Building (#406), Seminar Room 4122.
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Improving Image Deconvolution via Geometric Redundancies

Dr. Glenn Easley

System Planning Corportion

Abstract:   We propose to carry out image deconvolution by transforming the image matrix into geometrically redundant structures. Specific cases of these structures resemble the Radon transform. The two-dimensional deconvolution problem then reduces to a series of one-dimensional deconvolution problems for these projections. By estimating the projections using wavelet techniques, we are able to do deconvolution directly in a ridge let-like domain. We also show how this method can be carried out locally, so that deconvolution can be done in a curve let-like domain as well. These techniques suggest a whole new paradigm for developing deconvolution algorithms, which can incorporate leading deconvolution schemes. We conclude by showing experimental results indicating that these new algorithms can significantly improve upon current leading deconvolution methods. (In collaboration with Carlos Berenstein and Dennis Healy)