Tikhonov-Phillips regularization with operator dependent seminorms

We focus on the solution of discrete ill-posed problems to recover the original information from blurred signals in the presence of Gaussian white noise more accurately. We derive seminorms for the Tikhonov-Phillips regularization based on the underlying blur operator H. In this way it is possible to improve the reconstruction using spectral information of H. Reconstructions on various 1D discrete ill-posed inverse problems demonstrate the effect of the presented approach.