A memetic approach to discrete tomography from noisy projections

Discrete tomography deals with the reconstruction of images from very few projections, which is, in the general case, an NP-hard problem. This paper describes a new memetic reconstruction algorithm. It generates a set of initial images by network flows, related to two of the input projections, and lets them evolve towards a possible solution, by using crossover and mutation. Switch and compactness operators improve the quality of the reconstructed images during each generation, while the selection of the best images addresses the evolution to an optimal result. One of the most important issues in discrete tomography is known as the stability problem and it is tackled here, in the case of noisy projections, along four directions. Extensive experiments have been carried out to evaluate the robustness of the new methodology. A comparison with the output of two other evolutionary algorithms and a generalized version of a deterministic method shows the effectiveness of our new algorithm.