WHEN DOES THE RICHARDSON-LUCY DECONVOLUTION CONVERGE

We propose a simulation-based bootstrap method to access global signif icance levels of deconvolution models in the Richardson-Lucy and other iterative restoration algorithms that converge locally. These signifi cance levels allow one to check at each iterative step how good the mo del is and when iterations can be stopped. Adding more iterations in t he deconvolution improves the fitting but is very slow at later time; while too much entropy or smoothness will be lost in the models. A goo d deconvolution model should firstly have a significance level as high as possible (greater than or equal to 20%), and secondly, be as smoot h 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 t he likelihood of fitting and a priori entropy does not guarantee an ac ceptable significance level for the resulting model. If one's 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 iterat ive restoration algorithm can be performed later by acquiring a priori knowledge from the Richardson-Lucy restoration. However, this is nece ssary only when it does increase the levels significantly.