Theory of Multirate Signal Processing with Application to Signal and Image Reconstruction

Signal processing methods for signals sampled at different rates are investigated and applied to the problem of signal and image reconstruction or super-resolution reconstruction. The problem is approached from the viewpoint of linear mean-square estimation theory and multirate signal processing for one- and two-dimensional signals. A new look is taken at multirate system theory in one and two dimensions which provides the framework for these methodologies. A careful analysis of linear optimal filtering for problems involving different input and output sampling rates is conducted. This results in the development of index mapping techniques that simplify the formulation of Wiener-Hopf equations whose solution determine the optimal filters. The required filters exhibit periodicity in both one and two dimensions, due to the difference in sampling rates. The reconstruction algorithms developed are applied to one- and two-dimensional reconstruction problems.