Analysis of multiframe super-resolution reconstruction for image anti-aliasing and deblurring

Novel theoretical results for the super-resolution reconstruction (SRR) are presented under the case of arbitrary image warping. The SRR model is reasonably separated into two parts of anti-aliasing and deblurring. The anti-aliasing part is proved to be well-posed. The ill-posedness of the entire SRR process is shown to be mainly caused by the deblurring part. The motion estimation error results in a multiplicative perturbation to the warping matrix, and the perturbation bound is derived. The common regularization algorithms used in SRR are analyzed through the discrete Picard condition, which provides a theoretical measure for limits on SRR. Experiments and examples are supplied to validate the presented theories.