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Journal of Mathematical Imaging and Vision
Journal of Mathematical Imaging and Vision
Astronomical image restoration using an improved anisotropic diffusion
Pattern Recognition Letters
On Regularization Parameters Estimation in Edge---Preserving Image Reconstruction
ICCSA '08 Proceedings of the international conference on Computational Science and Its Applications, Part II
A Robust Method for Edge-Preserving Image Smoothing
ACIVS '08 Proceedings of the 10th International Conference on Advanced Concepts for Intelligent Vision Systems
Journal of Mathematical Imaging and Vision
Edge-Preserving Image Reconstruction with Wavelet-Domain Edge Continuation
ICIAR '09 Proceedings of the 6th International Conference on Image Analysis and Recognition
An evolutionary approach to inverse gray level quantization
VISUAL'07 Proceedings of the 9th international conference on Advances in visual information systems
An improved anisotropic diffusion model for detail- and edge-preserving smoothing
Pattern Recognition Letters
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IEEE Transactions on Image Processing
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SIAM Journal on Imaging Sciences
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Journal of Mathematical Imaging and Vision
A Simple Compressive Sensing Algorithm for Parallel Many-Core Architectures
Journal of Signal Processing Systems
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This paper is concerned with the reconstruction of images (or signals) from incomplete, noisy data, obtained at the output of an observation system. The solution is defined in maximum a posteriori (MAP) sense and it appears as the global minimum of an energy function joining a convex data-fidelity term and a Markovian prior energy. The sought images are composed of nearly homogeneous zones separated by edges and the prior term accounts for this knowledge. This term combines general nonconvex potential functions (PFs) which are applied to the differences between neighboring pixels. The resultant MAP energy generally exhibits numerous local minima. Calculating its local minimum, placed in the vicinity of the maximum likelihood estimate, is inexpensive but the resultant estimate is usually disappointing. Optimization using simulated annealing is practical only in restricted situations. Several deterministic suboptimal techniques approach the global minimum of special MAP energies, employed in the field of image denoising, at a reasonable numerical cost. The latter techniques are not directly applicable to general observation systems, nor to general Markovian prior energies. This work is devoted to the generalization of one of them, the graduated nonconvexity (GNC) algorithm, in order to calculate nearly-optimal MAP solutions in a wide range of situations. In fact, GNC provides a solution by tracking a set of minima along a sequence of approximate energies, starting from a convex energy and progressing toward the original energy. In this paper, we develop a common method to derive efficient GNC-algorithms for the minimization of MAP energies which arise in the context of any observation system giving rise to a convex data-fidelity term and of Markov random field (MRF) energies involving any nonconvex and/or nonsmooth PFs. As a side-result, we propose how to construct pertinent initializations which allow us to obtain meaningful solutions using local minimization of these MAP energies. Two numerical experiments-an image deblurring and an emission tomography reconstruction-illustrate the performance of the proposed technique