Discrete Tomography with Unknown Intensity Levels Using Higher-Order Statistics

Abstract

Discrete tomography focuses on the reconstruction of images containing only a limited number of different intensity values. Most of the methods assume that the intensities are a priori known. In practice, however, this information is usually not available. Therefore, the problem of the estimation of the intensity levels has been recently addressed by many researchers. In this paper, we present a novel approach for the tomographic reconstruction of binary images, when the two gray-levels are unknown. The problem is traced back to the minimization of an appropriate objective functional, in which a higher-order statistics-based discretization term enforces binary solutions. Instead of the gray-levels, the only parameter of this term is their mid-level value, which is iteratively approximated during the optimization process. Experiments on synthetic phantom images as well as on real data show that the proposed graduated optimization scheme can efficiently minimize the objective functional and the method provides accurate reconstructions. Compared to some of the state-of-the-art algorithms, the proposed method provides competitive results, while it requires less parameter settings, thus it can be considered as a valid alternative.