Abstract

Methods for super-resolution, which are implicitly optimization problems, frequently depend on the inversion of a matrix to obtain the solution. This step is ill-conditioned and usually demands, in practice, the evaluation of a regularized, pseudoinverse matrix. However, by specifying an appropriate energy function that, when minimized, yields an estimate of the pseudoinverse, one can investigate the possibility of implementing this regularized procedure on a fully connected architecture. The method is strictly rigorous in that the Moore–Penrose pseudoinverse is obtained in the limit of a large number of iterations. If a regularization parameter is explicitly introduced, or if a "settling accuracy" for the process is specified, a regularized pseudoinverse is readily calculated. We describe the advantages and disadvantages of such an approach and illustrate the use of this pseudoinverse in a variety of image reconstruction and recognition applications. This method thus provides the algorithm to be executed when and if the appropriate, fully parallel hardware is available.

© 1990 Optical Society of America