Multi-Parameter Regularization Methods for High-Resolution Image Reconstruction With Displacement Errors

We propose multi-parameter regularization methods for high-resolution image reconstruction which is described by an ill-posed problem. The regularization operator for the ill-posed problem is decomposed in a multiscale manner by using bi-orthogonal wavelets or tight frames. In the multiscale framework, for different scales of the operator we introduce different regularization parameters. These methods are analyzed under certain reasonable hypotheses. Numerical examples are presented to demonstrate the efficiency and accuracy of these methods.