Unsupervised Bayesian Convex Deconvolution Based on a Field With an Explicit Partition Function

• Published in: IEEE transactions on image processing Vol. 17; no. 1; pp. 16 - 26
• Main Author: Giovannelli, J.-F.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.01.2008; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Applied sciences; Artificial Intelligence; Bayes Theorem; Bayesian analysis; Bayesian methods; Bayesian statistics; Computational efficiency; Computational modeling; Computer simulation; convex potentials; Data processing; Deconvolution; Detection, estimation, filtering, equalization, prediction; Exact sciences and technology; Fast Fourier transforms; hyperparameters estimation; Image Enhancement - methods; Image Interpretation, Computer-Assisted - methods; Image processing; Information Storage and Retrieval - methods; Information, signal and communications theory; Markov processes; Mathematical analysis; Mathematical models; Monte Carlo methods; Monte-Carlo Markov chain; partition function; Partitions; Pattern Recognition, Automated - methods; regularization; Reproducibility of Results; Sampling methods; Sensitivity and Specificity; Signal and communications theory; Signal processing; Signal representation. Spectral analysis; Signal, noise; Simulated annealing; Statistics; Telecommunications and information theory; unsupervised estimation; Monte Carlo method; Parameter estimation; Monte-Carlo Markov chain; Probabilistic approach; hyperparameters estimation; regularization; Unsupervised classification; Markov model; Signal classification; Markov chain; Deconvolution; Partition function; Bayesian statistics; Gaussian field; Numerical simulation; convex potentials; Bayes methods; unsupervised estimation
• ISSN: 1057-7149; 1941-0042
• DOI: 10.1109/TIP.2007.911819

This paper proposes a non-Gaussian Markov field with a special feature: an explicit partition function. To the best of our knowledge, this is an original contribution. Moreover, the explicit expression of the partition function enables the development of an unsupervised edge-preserving convex deconvolution method. The method is fully Bayesian, and produces an estimate in the sense of the posterior mean, numerically calculated by means of a Monte-Carlo Markov chain technique. The approach is particularly effective and the computational practicability of the method is shown on a simple simulated example.