Fast maximum-likelihood image-restoration algorithms for three-dimensionalfluorescence microscopy

We have evaluated three constrained, iterative restoration algorithms to fi nd a fast, reliable algorithm for maximum-likelihood estimation of fluoresc ence microscopic images. Two algorithms used a Gaussian approximation to Po isson statistics, with variances computed assuming Poisson noise far the im ages. The third method used Csiszar's information-divergence. II-divergence ! discrepancy measure. Each method included a nonnegativity constraint and a penalty term for regularization; optimization was performed with a conjug ate gradient method. Performance of the methods was analyzed with simulated as well as biological images and the results compared with those obtained with the expectation-maximization-maximum-likelihood (EM-ML) algorithm. The I-divergence-based algorithm converged fastest and produced images similar to those restored by EM-ML as measured by several metrics. For a noiseless simulated specimen, the number of iterations required for the EM-X;IL meth od to reach a given log-likelihood value was approximately the square of th e number required for the I-divergence-based method to reach the same value . (C) 2001 Optical Society of America.