New methods for super-resolution

Abstract

This thesis presents a new, non-iterative method for super-resolution which we call the direct method. By exploiting the inherent structure of the discrete signal processing environment, the direct method reduces the discrete super-resolution problem to solving a linear set of equations. The direct method is shown to be closely related to the Gerchberg algorithm for super-resolution. A mathematical justification for early termination of the Gerchberg algorithm is presented and the design of optimal termination schemes is discussed. Another new super-resolution method, which we call the SVD method, is presented. The SVD method is based on the direct method and employs SVD techniques to minimize errors in the solution due to noise and aliasing errors on the known frequency samples. The new SVD method is shown to provide results nearly identical to the optimal solution given by the Gerchberg algorithm, with huge savings in time and computational work.