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.