Related papers: Discrete tomography reconstructions with small bou…
We consider possible reconstructions of a binary image of which the row and column sums are given. For any reconstruction we can define the length of the boundary of the image. In this paper we prove a new lower bound on the length of this…
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…
Discrete tomography deals with the reconstruction of images from projections collected along a few given directions. Different approaches can be considered, according to different models. In this paper we adopt the grid model, where pixels…
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…
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…
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…
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…
Inverse problems, such as accelerated MRI reconstruction, are ill-posed and an infinite amount of possible and plausible solutions exist. This may not only lead to uncertainty in the reconstructed image but also in downstream tasks such as…
We consider the reconstruction of a function on a finite subset of $\mathbb{Z}^2$ if the line sums in certain directions are prescribed. The real solutions form a linear manifold, its integer solutions a grid. First we provide an explicit…
Discrete tomography is concerned with the reconstruction of images that are defined on a discrete set of lattice points from their projections in several directions. The range of values that can be assigned to each lattice point is…
A set of orthonormal polynomials is proposed for image reconstruction from projection data. The relationship between the projection moments and image moments is discussed in detail, and some interesting properties are demonstrated.…
Binary tomography is concerned with reconstructing a binary image from a very small number or other limited CT projection data. This problem itself not only possesses several medical imaging applications but also can be considered a model…
Image reconstruction in X ray tomography consists in determining an object from its projections. In many applications such as non destructive testing, we look for an image who has a constant value inside a region (default) and another…
Tomographic reconstruction of a binary image from few projections is considered. A novel {\em heuristic} algorithm is proposed, the central element of which is a nonlinear transformation $\psi(p)=\log(p/(1-p))$ of the probability $p$ that a…
In this paper we will consider an unknown binary image, of which the length of the boundary and the area of the image are given. These two values together contain some information about the general shape of the image. We will study two…
Binary tomography is concerned with the recovery of binary images from a few of their projections (i.e., sums of the pixel values along various directions). To reconstruct an image from noisy projection data, one can pose it as a…
Discrete tomography deals with reconstructing finite spatial objects from lower dimensional projections and has applications for example in timetable design. In this paper we consider the problem of reconstructing a tile packing from its…
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…
Hybrid inverse problems such as Acousto-Electric Tomography, Current Density Imaging or Magnetic Resonance Electric Impedance Tomography are concerned with reconstructing the electrical conductivity from interior measurements. For a…
Continuous-domain visual signals are usually captured as discrete (digital) images. This operation is not invertible in general, in the sense that the continuous-domain signal cannot be exactly reconstructed based on the discrete image,…