Maximum likelihood restoration and choice of smoothing parameter in deconvolution of image data subject to Poisson noise

H. Malcolm Hudson, Thomas C. M. Lee

    Research output: Contribution to journalArticlepeer-review

    25 Citations (Scopus)

    Abstract

    Image degradation by blurring is a well-known phenomenon often described by the mathematical operation of convolution. Fourier methods are well developed for recovery, or restoration, of the true image from an observed image affected by convolution blur and additive constant variance Gaussian noise. One focus of this paper is to describe another statistical restoration method which is available when the image data exhibits Poisson variability. This is a common situation when counts of recorded activity form the image, as in medical imaging contexts. We apply Maximum Likelihood (ML) and Maximum Penalized Likelihood (MPL) procedures to deconvolve image data which has been degraded by blurring and Poisson variability in recorded activity. A second focus is formulation and comparison of automated selection procedures for regularization (smoothing) parameters in this context.

    Original languageEnglish
    Pages (from-to)393-410
    Number of pages18
    JournalComputational Statistics and Data Analysis
    Volume26
    Issue number4
    DOIs
    Publication statusPublished - 6 Feb 1998

    Keywords

    • cross-validation
    • deconvolution
    • fast computation
    • regularization
    • statistical algorithms

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