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

JOSA A, Vol. 18, Issue 5, pp. 1062-1071 (2001)

http://dx.doi.org/10.1364/JOSAA.18.001062

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### Abstract

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 Csiszár’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.

© 2001 Optical Society of America

**OCIS Codes**

(100.1830) Image processing : Deconvolution

(100.3020) Image processing : Image reconstruction-restoration

(100.3190) Image processing : Inverse problems

(100.6640) Image processing : Superresolution

(100.6890) Image processing : Three-dimensional image processing

(180.6900) Microscopy : Three-dimensional microscopy

**Citation**

Joanne Markham and José-Angel Conchello, "Fast maximum-likelihood image-restoration algorithms for three-dimensional fluorescence microscopy," J. Opt. Soc. Am. A **18**, 1062-1071 (2001)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-18-5-1062

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