Solution of the super-resolution problem by multi-valued nonlinear filtering, and its implementation using cellular neural networks

Abstract

An original approach to the solution of a super-resolution problem is considered. A solution is reduced to the iterative process by which the coefficients of the orthogonal spectrum corresponding to the highest frequencies, which are unknown, may be obtained. Supposing that unknown values of the signal are corrupted by uniform noise with the small dispersion, iterative procedure for obtaining the highest spectral coefficients is proposed. To remove the remaining noise, and to correct the spectral coefficients obtained in the first step, multi-valued nonlinear filters are proposed. Since the CNN with multi-valued neurons is the best instrument for an implementation of these filters, the corresponding templates are used.