Related papers: On the difference between solutions of discrete to…
We show that for n>2 the following equivalence problems are essentially the same: the equivalence problem for Lagrangians of order n with one dependent and one independent variable considered up to a contact transformation, a multiplication…
At a first glance, the problem of illuminating the boundary of a convex body by external light sources and the problem of covering a convex body by its smaller positive homothetic copies appear to be quite different. They are in fact two…
Single-image high dynamic range (SI-HDR) reconstruction has recently emerged as a problem well-suited for deep learning methods. Each successive technique demonstrates an improvement over existing methods by reporting higher image quality…
Common imaging techniques for detecting structural defects typically require sampling at more than twice the spatial frequency to achieve a target resolution. This study introduces a novel framework for imaging structural defects using…
In this paper, we present XctDiff, an algorithm framework for reconstructing CT from a single radiograph, which decomposes the reconstruction process into two easily controllable tasks: feature extraction and CT reconstruction.…
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…
We analyze integer linear programs which we obtain after discretizing two-dimensional subproblems arising from a trust-region algorithm for mixed integer optimal control problems with total variation regularization. We discuss NP-hardness…
We address the problem of bounding from below the self-intersection of integral curves on the projective plane blown-up at general points. In particular, by applying classical deformation theory we obtain the expected bound in the case of…
X-ray computed tomography (CT) is one of widely used diagnostic tools for medical and dental tomographic imaging of the human body. However, the standard filtered backprojection reconstruction method requires the complete knowledge of the…
In this paper we address the problem of matching two images with two different resolutions: a high-resolution image and a low-resolution one. The difference in resolution between the two images is not known and without loss of generality…
This paper concerns with nonuniform sampling and interpolation methods combined with variational models for the solution of a generalized image inpainting problem and the restoration of digital signals. In particular, we discuss the problem…
We give a recursive construction for projective Reed-Muller codes in terms of affine Reed-Muller codes and projective Reed-Muller codes in fewer variables. From this construction, we obtain the dimension of the subfield subcodes of…
Vector tomography methods intend to reconstruct and visualize vector fields in restricted domains by measuring line integrals of projections of these vector fields. Here, we deal with the reconstruction of irrotational vector functions from…
This work is concerned with applying iterative image reconstruction, based on constrained total-variation minimization, to low-intensity X-ray CT systems that have a high sampling rate. Such systems pose a challenge for iterative image…
Computed Tomography (CT) reconstruction is a fundamental component to a wide variety of applications ranging from security, to healthcare. The classical techniques require measuring projections, called sinograms, from a full 180$^\circ$…
In this work, we investigate the application of deep learning methods for computed tomography in the context of having a low-data regime. As motivation, we review some of the existing approaches and obtain quantitative results after…
In this paper, we introduce silhouette tomography, a novel formulation of X-ray computed tomography that relies only on the geometry of the imaging system. We formulate silhouette tomography mathematically and provide a simple method for…
I explain what is, what is not, and what is only sort of superresolution microscopy. I discuss optical resolution, first in terms of diffraction theory, then in terms of linear systems theory, and finally in terms of techniques that use…
This paper deals with a method of tomographic reconstruction of radially symmetric objects from a single radiograph, in order to study the behavior of shocked material. The usual tomographic reconstruction algorithms such as generalized…
The Levenshtein sequence reconstruction problem studies the reconstruction of a transmitted sequence from multiple erroneous copies of it. A fundamental question in this field is to determine the minimum number of erroneous copies required…