Sum of outer products dictionary learning for inverse problems

The data-driven adaptation of synthesis dictionaries has been exploited in many applications in signal processing and imaging. This paper exploits efficient methods for aggregate sparsity penalized dictionary learning by first approximating the matrix of image patches with a sum of sparse rank-one matrices (outer products) and then using a block coordinate descent approach to estimate the unknowns, and applies such sum of outer products methodologies for the problem of dictionary-blind image reconstruction. We propose efficient algorithms for adaptive image reconstruction and provide a convergence analysis for our methods. Our numerical experiments show the promising performance provided by the proposed schemes over recent methods in compressed sensing-based image reconstruction.

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