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Cancer therapy by hyperthermia treatment aims at heating up the region of the tumor while keeping the surrounding body below a prespeciied temperature. The heating is achieved by an electro{magnetic eld generated by several antennae which are placed around the patient. The hyperthermia problem asks to determine the parameters of the antennae, s.t. the resulting electro{magnetic eld is optimal with respect to some prescribed quality criterion. Iterative optimization algorithms require the solution of large, dense linear systems in each iteration step. We investigate modiications of standard regularization methods for inverse problems where the system matrix A is replaced by a family of sparse approximations fA k g. An adaptation strategy for choosing the approximation level, which leads to the same convergence rates as iteration schemes with the full matrix A, is proved. Wavelet compression techniques originally designed for applications in image processing are used to compute the approximating family fA k g leading to accelerated iteration schemes. They are nally applied to optimizing the hyperthermia treatment planning.

Wavelet-accelerated regularization methods for hyperthermia treatment planning