Related papers: On the difference between solutions of discrete to…
Considering a 2D matrix of positive and negative numbers, how might one draw a rectangle within it whose contents sum higher than all other rectangles'? This fundamental problem, commonly known the maximum rectangle problem or subwindow…
The problem of super-resolution in general terms is to recuperate a finitely supported measure $\mu$ given finitely many of its coefficients $\hat{\mu}(k)$ with respect to some orthonormal system. The interesting case concerns situations,…
In this paper, the problem of computing the projection, and therefore the minimum distance, from a point onto a Minkowski sum of general convex sets is studied. Our approach is based on the minimum norm duality theorem originally stated by…
Let a polyhedral convex set be given by a finite number of linear inequalities and consider the problem to project this set onto a subspace. This problem, called polyhedral projection problem, is shown to be equivalent to multiple objective…
The penetration power of x-rays allows one to image large objects. For example, centimeter-sized specimens can be imaged with micron-level resolution using synchrotron sources. In this case, however, the limited beam diameter and detector…
It is proved that the projection constants of two- and three-dimensional spaces are bounded by $4/3$ and $(1+\sqrt 5)/2$, respectively. These bounds are attained precisely by the spaces whose unit balls are the regular hexagon and…
We consider the geometric optics problem of finding a system of two reflectors that transform a spherical wavefront into a beam of parallel rays with prescribed intensity distribution. Using techniques from optimal transportation theory, it…
By suitably generalizing the Fourier constraint projection in the difference map phasing algorithm, an object can be reconstructed from its diffraction pattern even when the latter has been incoherently averaged over a discrete group of…
Images can vary according to changes in viewpoint, resolution, noise, and illumination. In this paper, we aim to learn representations for an image, which are robust to wide changes in such environmental conditions, using training pairs of…
Reconstruction of a 3D shape from a single 2D image is a classical computer vision problem, whose difficulty stems from the inherent ambiguity of recovering occluded or only partially observed surfaces. Recent methods address this challenge…
Assume you encounter an inverse problem that shall be solved for a large number of data, but no ground-truth data is available. To emulate this encounter, in this study, we assume it is unknown how to solve the imaging problem of Computed…
The effectiveness of projection methods for solving systems of linear inequalities is investigated. It is shown that they have a computational advantage over some alternatives and that this makes them successful in real-world applications.…
The inverse problem of diffraction theory in essence amounts to the reconstruction of the atomic positions of a solid from its diffraction image. From a mathematical perspective, this is a notoriously difficult problem, even in the…
The problem of image registration is finding a transformation that aligns two images, such that the corresponding points are in the same location. This paper introduces a simple, end-to-end trainable algorithm that is implementable in a few…
Binarization is widely used as an image preprocessing step to separate object especially text from background before recognition. For noisy images with uneven illumination such as degraded documents, threshold values need to be computed…
For structured-light range imaging, color stripes can be used for increasing the number of distinguishable light patterns compared to binary BW stripes. Therefore, an appropriate use of color patterns can reduce the number of light…
Image inverse problems have numerous applications, including image processing, super-resolution, and computer vision, which are important areas in image science. These application models can be seen as a three-function composite…
Solving the distributional worst-case in the distributionally robust optimization problem is equivalent to finding the projection onto the intersection of simplex and singly linear inequality constraint. This projection is a key component…
In this work, we consider a class of convex optimization problems in a real Hilbert space that can be solved by performing a single projection, i.e., by projecting an infeasible point onto the feasible set. Our results improve those…
A face image contains geometric cues in the form of configurational information and contours that can be used to estimate 3D face shape. While it is clear that 3D reconstruction from 2D points is highly ambiguous if no further constraints…