Related papers: A rigorous analysis using optimal transport theory…
In a recent article the authors showed that the radiative Transfer equations with multiple frequencies and scattering can be formulated as a nonlinear integral system. In the present article, the formulation is extended to handle reflective…
Curving beams are a promising new method for bypassing obstacles in future millimeter-wave to sub-terahertz (sub-THz) networks but lack a general predictive model for their reflections from arbitrary surfaces. We show that, unfortunately,…
We consider the problem of minimizing a convex function over the intersection of finitely many simple sets which are easy to project onto. This is an important problem arising in various domains such as machine learning. The main difficulty…
This paper considers the optimization-based traffic allocation problem among multiple end points in connectionless networks. The network utility function is modeled as a non-concave function, since it is the best description of the quality…
In the current book I suggest an off-road path to the subject of optimal transport. I tried to avoid prior knowledge of analysis, PDE theory and functional analysis, as much as possible. Thus I concentrate on discrete and semi-discrete…
The thesis concentrates on two problems in discrete geometry, whose solutions are obtained by analytic, probabilistic and combinatoric tools. The first chapter deals with the strong polarization problem. This states that for any sequence…
Spectral estimation can be preformed using the so called THREE-like approach. Such method leads to a convex optimization problem whose solution is characterized through its dual problem. In this paper, we show that the dual problem can be…
We establish a result which states that regularizing an inverse problem with the gauge of a convex set $C$ yields solutions which are linear combinations of a few extreme points or elements of the extreme rays of $C$. These can be…
We establish results for the injectivity and injectivity modulo gauge of certain inverse source problems in transport on a simply connected domain with variable index of refraction inducing a 'simple geometry'. The model given by radiative…
Removing undesired reflections from images taken through the glass is of great importance in computer vision. It serves as a means to enhance the image quality for aesthetic purposes as well as to preprocess images in machine learning and…
Employing tight-binding approximation we derive a transfer matrix formalism for one-dimensional single photon transport through a composite scattering center, which consists of parallel connected resonator optical waveguides. By solving the…
We revisit the Gray-Wyner lossy source coding problem and derive the first-order asymptotic optimal rate-distortion-perception region when additional perception constraints are imposed on reproduced source sequences. The optimal trade-off…
In this paper we study the high-dimensional super-resolution imaging problem. Here we are given an image of a number of point sources of light whose locations and intensities are unknown. The image is pixelized and is blurred by a known…
This paper constructs metalenses that separate homogeneous media with different refractive indices, refracting one domain into another while conserving a prescribed energy distribution. Using optimal transport theory, we design singlet and…
This article studies problems of optimal transport, by embedding them in a general functional analytic framework of convex optimization. This provides a unified treatment of a large class of related problems in probability theory and allows…
In this paper the optimal transport and the metamorphosis perspectives are combined. For a pair of given input images geodesic paths in the space of images are defined as minimizers of a resulting path energy. To this end, the underlying…
We consider an inverse source two-parameter sub-diffusion model subject to a nonlocal initial condition. The problem models several physical processes, among them are the microwave heating and light propagation in photoelectric cells. A…
Microscopy and optical imaging are drastically limited by the inhomogeneities encountered by the light while propagating from the object of interest to the detection system. In this context, adaptive optics and wavefront manipulation are…
Emerging quality requirements in modern optical systems increase the need for accurate simulation and compensation of disturbances. One key disturbance in high-power laser applications results from thermal loading due to absorption. This…
Optimal transport maps define a one-to-one correspondence between probability distributions, and as such have grown popular for machine learning applications. However, these maps are generally defined on empirical observations and cannot be…