Journal ArticleDOI
Prior Learning and Convex-Concave Regularization of Binary Tomography
TLDR
It is shown that the difference-of-convex-functions DC-programming framework is flexible enough to cope with this more general model class, and results show that reconstruction becomes feasible under conditions where the previous approach fails.About:
This article is published in Electronic Notes in Discrete Mathematics.The article was published on 2005-07-01. It has received 21 citations till now. The article focuses on the topics: Proximal gradient methods for learning & Regularization (mathematics).read more
Citations
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Journal ArticleDOI
DC programming and DCA: thirty years of developments
Hoai An Le Thi,Tao Pham Dinh +1 more
TL;DR: A short survey on thirty years of developments of DC (Difference of Convex functions) programming and DCA (DC Algorithms) which constitute the backbone of nonconvex programming and global optimization.
Journal ArticleDOI
A new efficient algorithm based on DC programming and DCA for clustering
TL;DR: A fast and robust algorithm based on DC (Difference of Convex functions) programming and DC Algorithms (DCA) is investigated and preliminary numerical solutions show the efficiency and the superiority of the appropriate DCA with respect to the standard K-means algorithm.
Journal ArticleDOI
Optimization based DC programming and DCA for hierarchical clustering
TL;DR: This paper proposes new optimization methods based on DC (Difference of Convex functions) programming for hierarchical clustering and demonstrates that the proposed algorithms are more efficient than related existing methods.
Journal ArticleDOI
Fuzzy clustering based on nonconvex optimisation approaches using difference of convex (DC) functions algorithms
TL;DR: A fast and robust nonconvex optimization approach for Fuzzy C-Means (FCM) clustering model based on DC (Difference of Convex functions) programming and DCA (DC Algorithms) that have been successfully applied in various fields of applied sciences, including Machine Learning.
References
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Journal ArticleDOI
Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images
Stuart Geman,Donald Geman +1 more
TL;DR: The analogy between images and statistical mechanics systems is made and the analogous operation under the posterior distribution yields the maximum a posteriori (MAP) estimate of the image given the degraded observations, creating a highly parallel ``relaxation'' algorithm for MAP estimation.
Journal ArticleDOI
On the statistical analysis of dirty pictures
TL;DR: In this paper, the authors proposed an iterative method for scene reconstruction based on a non-degenerate Markov Random Field (MRF) model, where the local characteristics of the original scene can be represented by a nondegenerate MRF and the reconstruction can be estimated according to standard criteria.
Book
Markov Random Field Modeling in Image Analysis
TL;DR: This detailed and thoroughly enhanced third edition presents a comprehensive study / reference to theories, methodologies and recent developments in solving computer vision problems based on MRFs, statistics and optimisation.
Mathematical methods in image reconstruction
Frank Natterer,Frank Wübbeling +1 more
TL;DR: This chapter discusses reconstruction algorithms, stability and resolution in tomography, and problems that have peculiarities in relation to nonlinear tomography.
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