Abstract

We propose in this paper an approach to perform the deconvolution of three-dimensional biological images obtained by fluorescence microscopy based on the Projection onto Convex Sets that is an important result from vector-space projections theory. We suggest the use of three sets of convex constraints where the first one is to perform the three-dimensional deconvolution, the second set is to perform super-resolution (partially recovery of the missing cone of frequencies) and the last one is to guarantee the positiveness of the solution. Due to the presence of Poisson noise in the images acquired by fluorescence microscopes using CCD cameras, we propose Goodman and Belsher's filter, which considers this kind of noise, to be used in the first set. In order to use the filter in a POCS methodology. it is pul in the form of a prototype image constraint. We have tested the algorithm using both synthetic and bead images and also with real cells images. The method was characterized by a fast convergence rate and also demonstrated a good performance in terms of both visual results and cost-benefit analysis.