Fast maximum-likelihood image-restoration algorithms for three-dimensional fluorescence microscopy

Joanne Markham, Jose Angel Conchello

Research output: Contribution to journalArticlepeer-review

45 Scopus citations


We have evaluated three constrained, iterative restoration algorithms to find a fast, reliable algorithm for maximum-likelihood estimation of fluorescence microscopic images. Two algorithms used a Gaussian approximation to Poisson statistics, with variances computed assuming Poisson noise for the images. The third method used Csiszair’s information-divergence (I-divergence) discrepancy measure. Each method included a nonnegativity constraint and a penalty term for regularization; optimization was performed with a conjugate 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-ML method to reach a given log-likelihood value was approximately the square of the number required for the I-divergence-based method to reach the same value.

Original languageEnglish
Pages (from-to)1062-1071
Number of pages10
JournalJournal of the Optical Society of America A: Optics and Image Science, and Vision
Issue number5
StatePublished - May 2001


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