Journal ArticleDOI
Adaptive Reconstruction of Discrete-Valued Objects from few Projections
TLDR
This paper describes how the binary reconstruction problem to multi-valued objects can be reconstructed just by combining binary decisions, and shows how approximately known absorption levels can be adaptively estimated within the reconstruction process.About:
This article is published in Electronic Notes in Discrete Mathematics.The article was published on 2005-07-01. It has received 17 citations till now. The article focuses on the topics: Discrete tomography & Combinatorial optimization.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.
Book ChapterDOI
Discrete tomography reconstruction based on the multi-well potential
TL;DR: A new discrete tomography reconstruction algorithm developed for reconstruction of images that consist of a small number of gray levels based on the minimization of the objective function which combines the regularized squared projection error with the multi-well potential function.
Journal ArticleDOI
Binary optimization for source localization in the inverse problem of ECG
TL;DR: A binary optimization approach to the transmembrane voltage (TMV)-based problem and a hybrid metaheuristic approach and the difference of convex functions (DC) algorithm were tested, showing their potential for application in ECGI.
Book ChapterDOI
An energy minimization reconstruction algorithm for multivalued discrete tomography
TL;DR: A new algorithm for multivalued discrete tomogra phy, that reconstructs images from few projections by approximating the minimum of a suitably constructed energy function with a deterministic optimization method is proposed.
References
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Journal ArticleDOI
Approximating Binary Images from Discrete X-Rays
TL;DR: This paper studies the problem of approximating binary images that are accessible only through few evaluations of their discrete X-ray transform, i.e., through their projections counted with multiplicity along some lines, and presents various approximation algorithms.
Journal ArticleDOI
Success and failure of certain reconstruction and uniqueness algorithms in discrete tomography
TL;DR: In this paper, various algorithms were presented for reconstructing and deciding (partial) uniqueness of finite lattice sets that are given by their discrete X-rays in a number m of directions.
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A Linear Programming Relaxation for Binary Tomography with Smoothness Priors
TL;DR: It is shown that the regularized LP-relaxation provides a good approximation and thus allows to bias the reconstruction towards solutions with spatially coherent regions, which provides an alternative to computationally expensive MCMC-sampling (Markov Chain Monte Carlo) techniques and other heuristic rounding schemes.
Journal ArticleDOI
Binary tomography on the hexagonal grid using gibbs priors
TL;DR: In this article, the problem of reconstructing a binary image (usually an image in the plane and not necessarily on a Cartesian grid) from a few projections translates into a problem of solving a system of equations which is very underdetermined and leads in general to a large class of solutions.
Journal ArticleDOI
Bayesian image reconstruction using image-modeling gibbs priors
TL;DR: In this paper, a Markov random field or Gibbs model was proposed for piecewise homogeneous images using not only low-order clique interactions to model homogeneity, but also high order clique interaction to model the continuity of borders in the images.