Deterministic discrete tomography reconstruction by energy minimization method on the triangular grid

• Binary tomography reconstruction problem for triangular grid is considered and analyzed.
• A new deterministic reconstruction method (SPG-T) is proposed.
• Experiments on hexagonal shape test images are presented and analyzed.
• Performance comparison of SPG-T with the stochastic reconstruction method (SA-T) is given.
• SPG-T method significantly outperform SA-T in both the quality of reconstructions and elapsed running times.

In this paper we consider the binary tomography reconstruction problem on the triangular grid. A deterministic energy-minimization method is proposed. The new method is based on the convex–concave regularization approach and uses the Spectral Projected Gradient optimization algorithm. The proposed method shows significant advantages, regarding the quality of the reconstructions and required running time, in comparison with the previously suggested reconstruction method based on the stochastic Simulated Annealing algorithm. Experimental results, using regular hexagon shaped test images, are presented and analyzed.