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

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....

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Veröffentlicht in:Computational statistics & data analysis 1998-02, Vol.26 (4), p.393-410
Hauptverfasser: Hudson, H.Malcolm, Lee, Thomas C.M.
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description 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.
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source RePEc; Elsevier ScienceDirect Journals
subjects Applied sciences
Artificial intelligence
Computer science
control theory
systems
Cross-validation
Deconvolution
Exact sciences and technology
Fast computation
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical approximation
Numerical methods in mathematical programming
Numerical methods in mathematical programming, optimization and calculus of variations
Numerical methods in optimization and calculus of variations
Numerical methods in probability and statistics
Parametric inference
Pattern recognition. Digital image processing. Computational geometry
Probability and statistics
Regularization
Sciences and techniques of general use
Statistical algorithms
Statistics
title Maximum likelihood restoration and choice of smoothing parameter in deconvolution of image data subject to Poisson noise
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