Acceleration of maximum-likelihood image restoration for fluorescence microscopy and other noncoherent imagery

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Abstract
Maximum-likelihood image restoration for noncoherent imagery, which is based on the generic expectation maximization (EM) algorithm of Dempster et al. [ J. R. Stat. Soc. B 39, 1 ( 1977)], is an iterative method whose convergence can be slow. We discuss an accelerative version of this algorithm. The EM algorithm is interpreted as a hill-climbing technique in which each iteration takes a step up the likelihood functional. The basic principle of the acceleration technique presented is to provide larger steps in the same vector direction and to find some optimal step size. This basic line-search principle is adapted from the research of Kaufman [ IEEE Trans. Med. Imag. MI-6, 37 ( 1987)]. Modifications to her original acceleration algorithm are introduced, which involve extensions in considering truncated data and an alternative way of implementing the search for an optimal step size. Log-likelihood calculations and reconstructed images from simulations show the execution time’s being shortened from the nonaccelerated algorithm by approximately a factor of 7.