Super-resolution through Error Energy Reduction

TLDR

The study introduces a novel perspective on extending a finite object's spectral segment. The authors formulate the problem as minimizing an implicit error energy in the truncated spectrum and devise a general‑purpose computer algorithm to achieve this reduction. The algorithm achieves super‑resolution beyond the diffraction limit and remains robust to noisy data.

Abstract

A new view of the problem of continuing a given segment of the spectrum of a finite object is presented. Based on this, the problem is restated in terms of reducing a defined ‘error energy’ which is implicit in the truncated spectrum. A computational procedure, which is readily implemented on general purpose computers, is devised which must reduce this error. It is demonstrated that by so doing, resolution well beyond the diffraction limit is attained. The procedure is shown to be very effective against noisy data.