On the superresolution limit in signal reconstruction

It is shown that there is an absolute limit to the improvement of resolution in signal reconstruction, compared with the classical Rayleigh or diffraction limits. The maximum achievable superresolution is determined by noise and can be derived from Shannon's theorem on the maximum rate of information transmission through a noisy channel. A maximum-likelihood algorithm is described which practically reaches the limit of resolution improvement, and the results of a check of the effectiveness of this algorithm by computer experiments and a nuclear magnetic resonance experiment are given. The relationship between superresolution and uncertainty is investigated. The superresolution is a logarithmic function of the signal-to-noise ratio.