Cancer therapy by hyperthermia treatment aims to heat up the region of the tumor while keeping the surrounding body below a prespecified temperature. The heating is achieved by an electromagnetic field generated by several antennae which are placed around the patient. The hyperthermia problem is to determine the parameters of the antennae, s.t. the resulting electromagnetic field 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 investigated modifications of standard regularization methods for inverse problems where the system matrix A is replaced by a family of sparse approximations {Ak}. 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 {Ak} leading to accelerated iteration schemes. They are finally applied to optimize hyperthermia treatment planning.