Related papers: Reflection methods for inverse problems with appli…
Our interest lies in developing some efficient methods for minimizing the sum of two geodesically convex functions on Hadamard manifolds, with the aim to enhance the convergence of the Douglas-Rachford algorithm in Hadamard manifolds.…
This work proposes a conformable fractional predictor-corrector algorithm for solving conformable fractional differential equations. Fractional calculus is finding applications in various scientific fields, but existing numerical methods…
We establish a region of convergence for the proto-typical non-convex Douglas-Rachford iteration which finds a point on the intersection of a line and a circle. Previous work on the non-convex iteration [2] was only able to establish local…
We prove that the Douglas--Rachford method applied to two closed convex cones in the Euclidean plane converges in finitely many steps if and only if the set of fixed points of the Douglas--Rachford operator is nontrivial. We analyze this…
The Douglas-Rachford algorithm is widely used in sparse signal processing for minimizing a sum of two convex functions. In this paper, we consider the case where one of the functions is weakly convex but the other is strongly convex so that…
The Douglas--Rachford method is a splitting method frequently employed for finding zeroes of sums of maximally monotone operators. When the operators in question are normal cones operators, the iterated process may be used to solve…
The reflection superposition phenomenon is complex and widely distributed in the real world, which derives various simplified linear and nonlinear formulations of the problem. In this paper, based on the investigation of the weaknesses of…
The task of reflection symmetry detection remains challenging due to significant variations and ambiguities of symmetry patterns in the wild. Furthermore, since the local regions are required to match in reflection for detecting a symmetry…
We prove that the sequences generate by the Douglas-Rachford method converge weakly to a solution of the inclusion problem
This paper addresses reflection removal, which is the task of separating reflection components from a captured image and deriving the image with only transmission components. Considering that the existence of the reflection changes the…
The Douglas-Rachford algorithm is a classical and powerful splitting method for minimizing the sum of two convex functions and, more generally, finding a zero of the sum of two maximally monotone operators. Although this algorithm is well…
The circumcentered-reflection method (CRM) has been applied for solving convex feasibility problems. CRM iterates by computing a circumcenter upon a composition of reflections with respect to convex sets. Since reflections are based on…
When imaging through a semi-reflective medium such as glass, the reflection of another scene can often be found in the captured images. It degrades the quality of the images and affects their subsequent analyses. In this paper, a novel deep…
We study the uniqueness and accuracy of the numerical solution of the problem of reconstruction of the shape and trajectory of a reflecting obstacle moving in an inhomogeneous medium from travel times, start and end points, and initial…
Many applications using large datasets require efficient methods for minimizing a proximable convex function subject to satisfying a set of linear constraints within a specified tolerance. For this task, we present a proximal projection…
Obtaining meaningful solutions for inverse problems has been a major challenge with many applications in science and engineering. Recent machine learning techniques based on proximal and diffusion-based methods have shown promising results.…
The Douglas--Rachford algorithm is a classic splitting method for finding a zero of the sum of two maximal monotone operators. It has also been applied to settings that involve one weakly and one strongly monotone operator. In this work, we…
The theory of specular X-ray reflectivity from a rough interface based upon the reflection function method (RFM) is proposed. The RFM transforms the second order differential equation for the wave amplitude into the non-linear first order…
The circumcentered Douglas--Rachford method (C--DRM), introduced by Behling, Bello Cruz and Santos, is an acceleration of the well-known Douglas-Rachford method (DRM) for finding the best approximation onto the intersection of finitely many…
Over the past decade, reflection matrix microscopy (RMM) and advanced image reconstruction algorithms have emerged to address the fundamental imaging depth limitations of optical microscopy in thick biological tissues and complex media. In…