Direct method for superresolution
David O. Walsh, Pamela A. Nielsen-Delaney · Journal of the Optical Society of America A · 1994
A noniterative method for superresolution is presented and analyzed. By exploiting the inherent structure of the discrete signal-processing environment, this algorithm reduces the problem of superresolution to that of solving a set of linear equations that relate known frequency samples to unknown time samples. It is shown that the algorithm always produces the correct solution if the known samples are error free and if the system is exactly determined or overdetermined. A technique to reduce the effect of measurement noise on the solution is presented also. It is shown that the noniterative algorithm will produce the same result as the Gerchberg–Papoulis algorithm [ Opt. Acta21, 709 ( 1974); IEEE Trans. Circuits Syst.CAS-22, 735 ( 1975)]. A simple, one-dimensional example is used to demonstrate the performance of both algorithms in the presence, and in the absence, of noise. The utility of the noniterative algorithm is demonstrated further with another one-dimensional example and then a two-dimensional example.