Fast algorithms for regularized minimum norm solutions to inverse problems

Abstract

The computational cost of solving biomedical inverse problems is extremely high. As a result, expensive high end computational platforms are required for processing and at times a trade-off must be made between accuracy and cost of computation. We present two fast computational algorithms for solving regularized inverse problems. The computational advantages are obtained by utilizing the extreme discrepancy between the dimension of the solution space and the measured data sets. The algorithms implement two common regularization procedures, Tikhonov regularization and truncated singular value decomposition (TSVD). The algorithms do not compromise the numerical accuracy of the solutions. Comparisons of costs of the conventional and proposed algorithms are given. Although the algorithms are presented in the context of biomedical inverse problems, they are applicable to any inverse problem with same characteristics, such as the geophysical inverse problems and non-destructive evaluation.