Given a rectangular array where entries represent the pixels of a digitalized image, we consider the problem of reconstructing an image from the number of occurrences of each color in every column and in every row. The complexity of this problem is still open when there are just three colors in the image. We study some special cases where the number of occurences of each color is limited to sma...

Super-resolution imaging aims at improving the resolution of an image by enhancing it with other images or data that might have been acquired using different imaging techniques or modalities. In this paper we consider the task of doubling the resolution of tomographic grayscale images of binary objects by fusion with double-resolution tomographic data that has been acquired from two viewing ang...

Our aim was to estimate the volumes of homogeneous structures whose contrast / intensity was changing with time, using only few (here 4) projections of the structures. Each projection was recorded over a period of time and consisted of a sequence of images. The projections of the structures were first separated by factor analysis of the total projections. Then each structure was reconstructed i...

The field of discrete tomography focuses on the reconstruction of samples that consist of only a few different materials. Ideally, a three-dimensional (3D) reconstruction of such a sample should contain only one grey level for each of the compositions in the sample. By exploiting this property in the reconstruction algorithm, either the quality of the reconstruction can be improved significantl...

We consider the reconstruction of a two-dimensional discrete image from a set of tomographic measurements corresponding to the Radon projection. Assuming that the image has a structure where neighbouring pixels have a larger probability to take the same value, we follow a Bayesian approach and introduce a fast messagepassing reconstruction algorithm based on belief propagation. For numerical re...

Tomography is an imaging technique to reconstruct cross-sections of objects from projection images in a non-destructive way. We have implemented two discrete tomographic (DT) reconstruction methods. The first method is general in the sense that the objects to be reconstructed are represented by pixels, and in this way the method can be used for reconstructing any shape. The second one is able t...

During the workshop entitled “Discrete Tomography”, held in Volkrange on March 22, 1999, A. Kuba presented the open problem of reconstructing discrete sets satisfying the properties of connectivity and convexity by projections taken along many directions. In this paper, we study this problem, considering a similar property of discrete sets: the Q-convexity. In fact this property contains a cert...

During the workshop entitled “Discrete Tomography”, held in Volkrange on March 22, 1999, A. Kuba presented the open problem of reconstructing discrete sets satisfying the properties of connectivity and convexity by projections taken along many directions. In this paper, we study this problem, considering a similar property of discrete sets: the Q-convexity. In fact this property contains a cert...

This paper studies the problem of reconstructing binary matrices that are only accessible through few evaluations of their discrete X-rays. Such question is prominently motivated by the demand in material science for developing a tool for the reconstruction of crystalline structures from their images obtained by high-resolution transmission electron microscopy. Various approaches have been sugg...