A mollifier method for linear operator equations of the first kind

An inversion method for the solution of ill-posed linear problems is presented. It is based on the idea of computing a mollified version of the searched-for solution and the approximate inverse operator is computed with exactly given quantities. The method is compared with known methods such as the Tikhonov-Phillips and Backus-Gilbert methods. Numerical tests verify the advantages, which are: no additional or artificial discretisation of the solution is needed, locally varying point-spread functions are easily realised, a simple change of the regularisation parameter with regard of a posteriori parameter strategies is implemented and a straightforward interpretation of the regularised solution is possible. When the approximation inversion operator is computed the solution can be computed by parallel processing.