Optimal Convergence Rates in Signal Recovery

Abstract

In the context of image analysis, the method of Fourier-domain processing is shown to yield restored signals of optimal quality. This confirms conjectures of statistical optimality that have been made in the past. Quality is measured in terms of convergence rates, and the influence of image smoothness on convergence rates is quantified. This influence is particularly interesting in the case of motion blur, where there is a critical degree of image smoothness (approximately four derivatives of the image) beyond which no improvement in restored image quality may be obtained by passing to smoother images. That is in marked contrast to the case of out-of-focus blur, where restored image quality is always greater for smoother images.