Accelerating sparse reconstruction for fast and precomputable system matrix inverses

Stanley J. Reeves

doi:10.1117/12.884583

7 February 2011 Accelerating sparse reconstruction for fast and precomputable system matrix inverses

Stanley J. Reeves

Proceedings Volume 7873, Computational Imaging IX; 78730V (2011) https://doi.org/10.1117/12.884583
Event: IS&T/SPIE Electronic Imaging, 2011, San Francisco Airport, California, United States

Abstract

Signal reconstruction using an l1-norm penalty has proven to be valuable in edge-preserving regularization as well as in sparse reconstruction problems. The developing field of compressed sensing typically exploits this approach to yield sparse solutions in the face of incoherent measurements. Unfortunately, sparse reconstruction generally requires significantly more computation because of the nonlinear nature of the problem and because the most common solutions damage any structure that may otherwise exist in the system matrix. In this work we adopt a majorizing function for the absolute value term that can be used with structured system matrices so that the regularization term in the matrix to be inverted does not destroy the structure of the original matrix. As a result, a system inverse can be precomputed and applied efficiently at each iteration to speed the estimation process. We demonstrate that this method can yield significant computational advantages when the original system matrix can be represented or decomposed into an efficiently applied singular value decomposition.

Citation Download Citation

Stanley J. Reeves "Accelerating sparse reconstruction for fast and precomputable system matrix inverses", Proc. SPIE 7873, Computational Imaging IX, 78730V (7 February 2011); https://doi.org/10.1117/12.884583

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