When Does the Richardson-Lucy Deconvolution Converge ?

Abstract

(\rl = Richardson-Lucy) We propose a simulation-based bootstrap method to access global significance levels of deconvolution models in the \rl and other iterative restoration algorithms that converge locally. These significance levels allow one to check at each iterative step how good the model is and when iterations can be stopped. Adding more iterations in the deconvolution improves the fitting but is very slow at later time; while too much entropy or smoothness will be lost in the models. A good deconvolution model should firstly have a significance level as high as possible ($\ge$ 20\%), and secondly, be as smooth as possible. We have used two examples to illustrate how such models can be derived in practice. We point out that maximizing the sum of the likelihood of fitting and {\em a priori} entropy does not guarantee an acceptable significance level for the resulting model. If one's {\em a priori} knowledge is too poor, the model may not be able to fit the data at a reasonable significance level. Instead, a maximum-entropy-like iterative restoration algorithm can be performed later by acquiring {\em a priori} knowledge from the \rl restoration. However, this is necessary only when it does increase the levels significantly.