Variable-smoothing regularization methods for inverse problems

Patricia K. Lamm
Department of Mathematics
Michigan State University
E. Lansing, MI 48824-1027


Theory and Practice of Control and Systems, A. Tornambe, G. Conte, and A. M. Perdon, Editors; World Scientific, 1999.

Abstract: Many inverse problems of practical interest are ill-posed in the sense that solutions do not depend continuously on data. To effectively solve such problems, regularization methods are typically used. One problem associated with classical regularization methods is that the solution may be oversmoothed in the process. We present an alternative ``local regularization'' approach in which a decomposition of the problem into ``local'' and ``global'' parts permits varying amounts of local smoothing to be applied over the domain of the solution. This allows for more regularization in regions where the solution is likely to be more smooth, and less regularization in regions where sharp features are likely to be present. We illustrate this point with several numerical examples.

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Contact: lamm@math.msu.edu