Related papers: Reflection methods for inverse problems with appli…
We present a new computation method for simulating reflection high-energy electron diffraction and the total-reflection high-energy positron diffraction experiments. The two experiments are used commonly for the structural analysis of…
Serial crystallography experiments routinely produce thousands of diffraction patterns from crystals in random orientations. To turn this stream of images into a usable dataset, each pattern must be indexed before integration and merging…
Undoing the image formation process and therefore decomposing appearance into its intrinsic properties is a challenging task due to the under-constraint nature of this inverse problem. While significant progress has been made on inferring…
The differential cross-section for the reflection of light beams off rigid bodies obtained by the rotation of a generic derivable convex function is calculated. The calculation is developed using elementary notions of calculus and is…
The Douglas-Rachford algorithm is one of the most prominent splitting algorithms for solving convex optimization problems. Recently, the method has been successful in finding a generalized solution (provided that one exists) for…
In this paper, we propose a new algorithm combining the Douglas-Rachford (DR) algorithm and the Frank-Wolfe algorithm, also known as the conditional gradient (CondG) method, for solving the classic convex feasibility problem. Within the…
This work is concerned with the convergence rate analysis of the Douglas-Rachford splitting (DRS) method for finding a zero of the sum of two maximally monotone operators. We obtain an exact rate of convergence for the DRS algorithm and…
We study the convergence of the Method of Reflections for the Dirichlet problem of the Poisson and the Stokes equations in perforated domains which consist in the exterior of balls. We prove that the method converges if the balls are…
We introduce a novel method for using reflectance to identify materials. Reflectance offers a unique signature of the material but is challenging to measure and use for recognizing materials due to its high-dimensionality. In this work,…
Let $E$ be a complete, separable metric space and $A$ be an operator on $C_b(E)$. We give an abstract definition of viscosity sub/supersolution of the resolvent equation $\lambda u-Au=h$ and show that, if the comparison principle holds,…
In this paper, we present a Douglas-Rachford splitting algorithm within a Hilbert space framework that yields a projected solution for a quasi-variational inequality. This is achieved under the conditions that the operator associated with…
Fourier-domain Difference Map (FDM) for phase retrieval with two oversampled coded diffraction patterns are proposed. FDM is a 3-parameter family of fixed point algorithms including Fourier-domain Hybrid-Projection-Reflection (FHPR) and…
Reconfigurable reflectors have a significant potential in future telecommunication systems, and approaches to the design and realization of full and tunable reflection control are now actively studied. Reflectarrays, being the classical…
We adapt the Douglas-Rachford (DR) splitting method to solve nonconvex feasibility problems by studying this method for a class of nonconvex optimization problem. While the convergence properties of the method for convex problems have been…
In view of the great performance of circumcentered isometry methods for solving the best approximation problem, in this work we further investigate the locally proper circumcenter mapping and circumcentered method. Various examples of…
Inverse problems have many applications in science and engineering. In Computer vision, several image restoration tasks such as inpainting, deblurring, and super-resolution can be formally modeled as inverse problems. Recently, methods have…
In this work, we propose some new Douglas-Rashford splitting algorithms for solving a class of generalized DC (difference of convex functions) in real Hilbert spaces. The proposed methods leverage the proximal properties of the nonsmooth…
Recently, several convergence rate results for Douglas-Rachford splitting and the alternating direction method of multipliers (ADMM) have been presented in the literature. In this paper, we show global linear convergence rate bounds for…
A general fusion method to find solutions to the reflection equation in higher spin representations starting from the fundamental one is shown. The method is illustrated by applying it to obtaining the $K$ diagonal boundary matrices in an…
In this paper, we present a dimension reduction method to reduce the dimension of parameter space and state space and efficiently solve inverse problems. To this end, proper orthogonal decomposition (POD) and radial basis function (RBF) are…