An outline of adaptive wavelet Galerkin methods for Tikhonov regularization of inverse parabolic problems

In this paper, we discuss some ideas how adaptive wavelet schemes can be applied to the treatment of certain inverse problems. The classical Tikhonov-Phillips regularization produces a numerical scheme which consists of an inner and an outer iteration. In its normal form, the inner iteration can be interpreted as a boundedly invertible operator equation which can be handled very efficiently by using a stable wavelet basis. This general framework is illustrated by an application to the inverse heat equation.