The task of reconstructing binary images from the knowledge of their line sums (discrete X-rays) in a given finite number m of directions is ill-posed. Even some small noise in the physical measurements can lead to dramatically different yet still unique solutions. The present paper addresses in particular the following problems. Does discrete tomography have the power of error correction? Can ...

Filtered Back Projection and Simultaneous Iterative Reconstruction Technique (SIRT) are the most popular reconstruction algorithms in electron tomography. In both cases every TEM image is smeared back into object space along the original pathway (so-called back-projection). Both methods produce a blurring of the reconstructed objects, which affects the segmentation step after reconstruction. Fo...

The so-called 3DXRD microscope, implemented at the European Synchrotron Radiation Facility in Grenoble, France, utilizes the principle of X-ray diffraction for mapping the crystalline grains within hard materials such as metals or ceramics. Present algorithms, using continuous models, roughly reconstruct the image from diffraction data, but they are often unable to assign unambiguous values to ...

We present a novel approach to the tomographic reconstruction of binary objects from few projection directions within a limited range of angles. A quadratic objective functional over binary variables comprising the squared projection error and a prior penalizing non-homogeneous regions, is supplemented with a concave functional enforcing binary solutions.Application of a primal-dual subgradient...

We present a non-convex variational approach to non-binary discrete tomography which combines non-local projection constraints with a continuous convex relaxation of the multilabeling problem. Minimizing this non-convex energy is achieved by a fixed point iteration which amounts to solving a sequence of convex problems, with guaranteed convergence to a critical point. A competitive numerical ev...

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 compactn...

This paper introduces a parametric level-set method for tomographic reconstruction of partially discrete images. Such images consist of a continuously varying background and an anomaly with a constant (known) grey-value. We express the geometry of the anomaly using a level-set function, which we represent using radial basis functions. We pose the reconstruction problem as a bi-level optimizatio...

A kind of fixed-point problem in the area of discrete tomography is proposed and investigated. Our chief concern in this paper is the case of square windows in the plane. Dealing with the arrays which are bounded, of polynomial growth, and finite-ring-valued, one comes across several interesting phenomena of combinatorial and arithmetic nature. keywords: discrete tomography; fixed point; square...

Discrete electron tomography is a new approach for three-dimensional reconstruction of nanoscale objects. The technique exploits prior knowledge of the object to be reconstructed, which results in an improvement of the quality of the reconstructions. Through the combination of conventional transmission electron microscopy and discrete electron tomography with a model-based approach, quantitativ...

BACKGROUND The Filtered Back-Projection (FBP) algorithm is the most important technique for computerized tomographic (CT) imaging, in which the ramp filter plays a key role. FBP algorithm had been derived using the continuous system model. However, it has to be discretized in practical applications, which necessarily produces distortion in the reconstructed images. METHODS A novel scheme is p...