International Journal of Computer Vision
Statistical approaches in quantitative positron emissiontomography
Statistics and Computing
Hidden Markov Random Field Model Selection Criteria Based on Mean Field-Like Approximations
IEEE Transactions on Pattern Analysis and Machine Intelligence
Estimating Optimal Parameters for MRF Stereo from a Single Image Pair
IEEE Transactions on Pattern Analysis and Machine Intelligence
Computational Statistics & Data Analysis
A non-local regularization strategy for image deconvolution
Pattern Recognition Letters
Image matting based on local color discrimination by SVM
Pattern Recognition Letters
SAR image regularization with fast approximate discrete minimization
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
Computational Statistics & Data Analysis
Computational Biology and Chemistry
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The parameters of the prior, the hyperparameters, play an important role in Bayesian image estimation. Of particular importance for the case of Gibbs priors is the global hyperparameter, β, which multiplies the Hamiltonian. Here we consider maximum likelihood (ML) estimation of β from incomplete data, i.e., problems in which the image, which is drawn from a Gibbs prior, is observed indirectly through some degradation or blurring process. Important applications include image restoration and image reconstruction from projections. Exact ML estimation of β from incomplete data is intractable for most image processing. Here we present an approximate ML estimator that is computed simultaneously with a maximum a posteriori (MAP) image estimate. The algorithm is based on a mean field approximation technique through which multidimensional Gibbs distributions are approximated by a separable function equal to a product of one-dimensional (1-D) densities. We show how this approach can be used to simplify the ML estimation problem. We also show how the Gibbs-Bogoliubov-Feynman (GBF) bound can be used to optimize the approximation for a restricted class of problems. We present the results of a Monte Carlo study that examines the bias and variance of this estimator when applied to image restoration