A segmentation-based regularization term for image deconvolution

• Published in: IEEE transactions on image processing 2006-07, Vol.15 (7), p.1973-1984
• Main Author: Mignotte, M.
• Format: Article
• Language: English
• Subjects: Adaptive prior model; Additive noise; Algorithms; Applied sciences; Artificial Intelligence; Bayes Theorem; Bayesian analysis; Bayesian estimation; Bayesian methods; Benchmark testing; Computer Simulation; Deconvolution; Degradation; Detection, estimation, filtering, equalization, prediction; Estimates; Exact sciences and technology; Gaussian noise; image deconvolution or restoration; Image Enhancement - methods; Image Interpretation, Computer-Assisted - methods; Image processing; Image restoration; Image segmentation; Information Storage and Retrieval - methods; Information, signal and communications theory; Markov Chains; Markovian model; Mathematical models; Maximum likelihood estimation; Models, Statistical; Pattern Recognition, Automated - methods; Performance evaluation; Regression Analysis; Regularization; Reproducibility of Results; Restoration; Segmentation; Sensitivity and Specificity; Signal and communications theory; Signal processing; Signal representation. Spectral analysis; Signal, noise; Studies; Telecommunications and information theory; Tikhonov regularization
• ISSN: 1057-7149; 1941-0042
• DOI: 10.1109/TIP.2006.873446

This paper proposes a new and original inhomogeneous restoration (deconvolution) model under the Bayesian framework for observed images degraded by space-invariant blur and additive Gaussian noise. In this model, regularization is achieved during the iterative restoration process with a segmentation-based a priori term. This adaptive edge-preserving regularization term applies a local smoothness constraint to pre-estimated constant-valued regions of the target image. These constant-valued regions (the segmentation map) of the target image are obtained from a preliminary Wiener deconvolution estimate. In order to estimate reliable segmentation maps, we have also adopted a Bayesian Markovian framework in which the regularized segmentations are estimated in the maximum a posteriori (MAP) sense with the joint use of local Potts prior and appropriate Gaussian conditional luminance distributions. In order to make these segmentations unsupervised, these likelihood distributions are estimated in the maximum likelihood sense. To compute the MAP estimate associated to the restoration, we use a simple steepest descent procedure resulting in an efficient iterative process converging to a globally optimal restoration. The experiments reported in this paper demonstrate that the discussed method performs competitively and sometimes better than the best existing state-of-the-art methods in benchmark tests.