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.
Text of paper:
Contact: lamm@math.msu.edu