The discrete Radon transform and its approximate inversion via linear programming
Discrete Applied Mathematics
Mathematical methods in image reconstruction
Mathematical methods in image reconstruction
A D. C. Optimization Algorithm for Solving the Trust-Region Subproblem
SIAM Journal on Optimization
Approximating Binary Images from Discrete X-Rays
SIAM Journal on Optimization
A branch and reduce approach for solving a class of low rank d.c. programs
Journal of Computational and Applied Mathematics
Grey level estimation for discrete tomography
DGCI'09 Proceedings of the 15th IAPR international conference on Discrete geometry for computer imagery
Reconstruction from limited-angle projections based on δ - u spectrum analysis
IEEE Transactions on Image Processing
A semi-automatic algorithm for grey level estimation in tomography
Pattern Recognition Letters
Discrete tomography reconstruction based on the multi-well potential
IWCIA'11 Proceedings of the 14th international conference on Combinatorial image analysis
Direction-dependency of binary tomographic reconstruction algorithms
Graphical Models
A network flow algorithm for binary image reconstruction from few projections
DGCI'06 Proceedings of the 13th international conference on Discrete Geometry for Computer Imagery
A benchmark evaluation of large-scale optimization approaches to binary tomography
DGCI'06 Proceedings of the 13th international conference on Discrete Geometry for Computer Imagery
Direction-dependency of a binary tomographic reconstruction algorithm
CompIMAGE'10 Proceedings of the Second international conference on Computational Modeling of Objects Represented in Images
Binary tomography with deblurring
IWCIA'06 Proceedings of the 11th international conference on Combinatorial Image Analysis
A neural network approach to real-time discrete tomography
IWCIA'06 Proceedings of the 11th international conference on Combinatorial Image Analysis
Image Reconstruction from Sparse Projections Using S-Transform
Journal of Mathematical Imaging and Vision
Projection selection dependency in binary tomography
Acta Cybernetica
Dynamic angle selection in binary tomography
Computer Vision and Image Understanding
A method for feature detection in binary tomography
DGCI'13 Proceedings of the 17th IAPR international conference on Discrete Geometry for Computer Imagery
Bounds on the quality of reconstructed images in binary tomography
Discrete Applied Mathematics
Approximate Discrete Reconstruction Algorithm
Fundamenta Informaticae - Strategies for Tomography
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We present a novel approach to the tomographic reconstruction of binary objects from few projection directions within a limited range of angles. A quadratic objective functional over binary variables comprising the squared projection error and a prior penalizing non-homogeneous regions, is supplemented with a concave functional enforcing binary solutions. Application of a primal-dual subgradient algorithm to a suitable decomposition of the objective functional into the difference of two convex functions leads to an algorithm which provably converges with parallel updates to binary solutions. Numerical results demonstrate robustness against local minima and excellent reconstruction performance using five projections within a range of 90^@?. Our approach is applicable to quite general objective functions over binary variables with constraints and thus applicable to a wide range of problems within and beyond the field of discrete tomography.