Regularized binary tomography on the hexagonal grid

Abstract

The tomography reconstruction problem on continuous domain can be considered as an inverse Radon transform problem, which is, in general case, ill-posed. Therefore, good solutions proposed in continuous space, like total variation (TV) type regularization, are often adapted in discrete space of digital images. In this paper, we consider the binary tomography reconstruction problem of images on the hexagonal grid. The proposed algorithm uses energy minimization technique to find (near) optimal solution. The suggested regularization term uses the neighbor relation of the hexagonal grid such that each difference of two closest neighbor hexels is included exactly once—this is motivated by the TV on the square grid. Experimental results on a number of test images are presented and analyzed. Comparison of the obtained results with results provided by the already proposed stochastic type method based on Gibbs priors is also included. The new method shows advantage in both aspects, quality of the reconstructions and running time.