Matrix computations (3rd ed.)
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 continuous approach for the concave cost supply problem via DC programming and DCA
Discrete Applied Mathematics
A Network Flow Algorithm for Reconstructing Binary Images from Continuous X-rays
Journal of Mathematical Imaging and Vision
On image reconstruction algorithms for binary electromagnetic geotomography
Theoretical Computer Science
Limited view CT reconstruction and segmentation via constrained metric labeling
Computer Vision and Image Understanding
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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.