The method we present in this paper has been motivated by a restoration problem in a tomography context. We are interested in blurred and noised binary images restoration. We consider the discrete version of a minimization problem settled in the space of bounded variation functions. We give a general abstract formulation of the (discrete) optimization problem with binary constraints and provide...

The present paper deals with the discrete inverse problem of reconstructing binary matrices from their row and column sums under additional constraints on the number and pattern of entries in specified minors. While the classical consistency and reconstruction problems for two directions in discrete tomography can be solved in polynomial time, it turns out that these window constraints cause va...

One of the basic problems in discrete tomography is the reconstruction of discrete sets from few projections. Assuming that the set to be reconstructed fulfills some geometrical properties is a commonly used technique to reduce the number of possibly many different solutions of the same reconstruction problem. The class of hv-convex discrete sets and its subclasses have a well-developed theory....

In this paper we prove several new stability results for the reconstruction of binary images from two projections. We consider an original image that is uniquely determined by its projections and possible reconstructions from slightly different projections. We show that for a given difference in the projections, the reconstruction can only be disjoint from the original image if the size of the ...

A control rod K5 of the 10 MW Budapest Research Reactor was damaged in 2004. We have applied both neutron and X-ray radiography to study the distribution of the residual material in the damaged K5. X-ray radiography visualized the main distribution of the residual materials, like different kinds of B4C and water, and the frozen gas bubbles, while neutron radiography displayed the fine structure...

We consider the problem of reconstructing binary images from their horizontal and vertical projections. We present a condition that the projections must necessarily satisfy when there exist two disjoint reconstructions from those projections. More generally, we derive an upper bound on the symmetric difference of two reconstructions from the same projections. We also consider two reconstruction...

The notions of minimality, π -uniqueness and additivity originated in discrete tomography. They have applications to Kronecker products of characters of the symmetric group and arise as the optimal solutions of quadratic transportation problems. Here, we introduce the notion of real-minimality and give geometric characterizations of all these notions for a matrix A, by considering the intersect...

We consider the problem of reconstructing binary images from their horizontal and vertical projections. It is known that the projections do not necessarily determine the image uniquely. In a previous paper it was shown that the symmetric difference between two solutions (binary images that satisfy the projections) is at most 4α √ 2N . Here N is the sum of the projections in one direction (i.e. ...

Abstract. Digital tomography deals with the problem of reconstructing an image from its projections. The image may or may not be reconstructible uniquely. The effective reconstruction also depends on the kind of projections taken. We consider the simplest two-dimensional case in which we have a 2D matrix and the projections are orthogonal. The matrices which are not uniquely reconstructible are...