Related papers: On the difference between solutions of discrete to…
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…
We consider the problem of reconstructing binary images from their horizontal and vertical projections. For any reconstruction we define the length of the boundary of the image. In this paper we assume that the projections are monotone, and…
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…
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 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…
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…
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…
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…
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…
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,…
In dynamic tomography the object undergoes changes while projections are being acquired sequentially in time. The resulting inconsistent set of projections cannot be used directly to reconstruct an object corresponding to a time instant.…
English: This paper concerns the image reconstruction from a few projections in Computed Tomography (CT). The main objective of this paper is to show that the problem is so ill posed that no classical method, such as analytical methods…
We study the duality of reconstruction systems, which are $g$-frames in a finite dimensional setting. These systems allow redundant linear encoding-decoding schemes implemented by the so-called dual reconstruction systems. We are…
In this paper we address the problem of visual quality of images reconstructed from block-wise random projections. Independent reconstruction of the blocks can severely affect visual quality, by displaying artifacts along block borders. We…
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.…
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…
In this note we study the connection between the existence of a projective reconstruction and the existence of a fundamental matrix satisfying the epipolar constraints.
The reconstruction problem in electrical impedance tomography is highly ill-posed, and it is often observed numerically that reconstructions have poor resolution far away from the measurement boundary but better resolution near the…
We consider the visual disambiguation task of determining whether a pair of visually similar images depict the same or distinct 3D surfaces (e.g., the same or opposite sides of a symmetric building). Illusory image matches, where two images…
Although Neural Differential Equations have shown promise on toy problems such as MNIST, they have yet to be successfully applied to more challenging tasks. Inspired by variational methods for image restoration relying on partial…