Related papers: Reflection methods for inverse problems with appli…
More than 40 years ago, Lions and Mercier introduced in a seminal paper the Douglas-Rachford algorithm. Today, this method is well recognized as a classical and highly successful splitting method to find minimizers of the sum of two (not…
Light reflection plays a crucial role in a number of modern technologies. In this paper, analytical expressions for maximal reflected power in any direction and for any polarization are given for generic planar structures made of a single…
Reflectional symmetry is ubiquitous in nature. While extrinsic reflectional symmetry can be easily parametrized and detected, intrinsic symmetry is much harder due to the high solution space. Previous works usually solve this problem by…
In this work we investigate the possibility of using the reflection algebra as a source of functional equations. More precisely, we obtain functional relations determining the partition function of the six-vertex model with domain-wall…
Douglas-Rachford splitting and the alternating direction method of multipliers (ADMM) can be used to solve convex optimization problems that consist of a sum of two functions. Convergence rate estimates for these algorithms have received…
Understanding how proteins structurally interact is crucial to modern biology, with applications in drug discovery and protein design. Recent machine learning methods have formulated protein-small molecule docking as a generative problem…
Specular reflections pose a significant challenge for object segmentation, as their sharp intensity transitions often mislead both conventional algorithms and deep learning based methods. However, as the specular reflection must lie on the…
This work develops new numerical methods for the solution of the tomography problem in domains with reflecting obstacles. We compare the solution's performance for Lambertian reflection, for classical tomography with ubroken rays and for…
We report on progress in algorithms for iterative phase retrieval. The theory of convex optimization is used to develop and to gain insight into counterparts for the nonconvex problem of phase retrieval. We propose a relaxation of averaged…
We present a convolutional approach to reflection symmetry detection in 2D. Our model, built on the products of complex-valued wavelet convolutions, simplifies previous edge-based pairwise methods. Being parameter-centered, as opposed to…
We present an approach for the study and design of reflectors with rotational or translational symmetry that redirect light from a point source into any desired radiant intensity distribution. This method is based on a simple conformal map…
The Douglas-Rachford algorithm (DRA) is a powerful optimization method for minimizing the sum of two convex (not necessarily smooth) functions. The vast majority of previous research dealt with the case when the sum has at least one…
In this article, we propose and study a stochastic and relaxed preconditioned Douglas--Rachford splitting method to solve saddle-point problems that have separable dual variables. We prove the almost sure convergence of the iteration…
This work develops new numerical methods for the solution of the tomography problem in domains with reflecting obstacles. We compare the solution's performance for Lambertian reflection, for classical tomography with unbroken rays and for…
Consider a reflected diffusion on the positive half-line. We approximate it by solutions of stochastic differential equations using the penalty method: We emulate the "hard barrier" of reflection by a "soft barrier" of a large drift…
The basic optimization problem of road design is quite challenging due to a objective function that is the sum of nonsmooth functions and the presence of set constraints. In this paper, we model and solve this problem by employing the…
The Douglas-Rachford splitting method is a classical and widely used algorithm for solving monotone inclusions involving the sum of two maximally monotone operators. It was recently shown to be the unique frugal, no-lifting…
In this position paper, we consider the state of computer vision research with respect to invariance to the horizontal orientation of an image -- what we term reflection invariance. We describe why we consider reflection invariance to be an…
We tackle the problem of reflectance estimation from a set of multi-view images, assuming known geometry. The approach we put forward turns the input images into reflectance maps, through a robust variational method. The variational model…
Deep learning-based models have demonstrated remarkable success in solving illposed inverse problems; however, many fail to strictly adhere to the physical constraints imposed by the measurement process. In this work, we introduce a…