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We present a new inner-outer iterative algorithm for edge enhancement in imaging problems. At each outer iteration, we formulate a Tikhonov-regularized problem where the penalization is expressed in the 2-norm and involves a regularization…
Recovering high quality surfaces from noisy triangulated surfaces is a fundamental important problem in geometry processing. Sharp features including edges and corners can not be well preserved in most existing denoising methods except the…
This paper presents a regularized Newton method (RNM) with generalized regularization terms for unconstrained convex optimization problems. The generalized regularization includes quadratic, cubic, and elastic net regularizations as special…
We propose a regularization for Reduced Order Models (ROMs) of the quasi-geostrophic equations (QGE) to increase accuracy when the Proper Orthogonal Decomposition (POD) modes retained to construct the reduced basis are insufficient to…
This paper addresses the inverse scattering problem in the domain Omega. The input data, measured outside Omega, involve the waves generated by the interaction of plane waves with various directions and unknown scatterers fully occluded…
Corrections to scaling in the 3D Ising model are studied based on Monte Carlo (MC) simulation results for very large lattices with linear lattice sizes up to L=3456. Our estimated values of the correction-to-scaling exponent omega tend to…
We present a new empirical model for galaxy rotation curves that introduces a velocity correction term {\omega}, derived from observed stellar motion and anchored to Keplerian baselines. Unlike parametric halo models or modified gravity…
Many key algorithms in 3-manifold topology involve the enumeration of normal surfaces, which is based upon the double description method for finding the vertices of a convex polytope. Typically we are only interested in a small subset of…
We consider the sign problem for classical spin models at complex $\beta =1/g_0^2$ on $L\times L$ lattices. We show that the tensor renormalization group method allows reliable calculations for larger Im$\beta$ than the reweighting Monte…
This work presents a novel regularization method for the identification of Nonlinear Autoregressive eXogenous (NARX) models. The regularization method promotes the exponential decay of the influence of past input samples on the current…
The Rayleigh conjecture about convergence up to the boundary of the series representing the scattered field in the exterior of an obstacle $D$ is widely used by engineers in applications. However this conjecture is false for some obstacles.…
Regularization is a critical technique for ensuring well-posedness in solving inverse problems with incomplete measurement data. Traditionally, the regularization term is designed based on prior knowledge of the unknown signal's…
We present two new analytic formulations of the Density Matrix Renormalization Group Method. In these formulations we combine the block renormalization group (BRG) procedure with Variational and Fokker-Planck methods. The BRG method is used…
In this paper, we propose a method, called GridFace, to reduce facial geometric variations and improve the recognition performance. Our method rectifies the face by local homography transformations, which are estimated by a face…
Adaptive cubic regularization methods have emerged as a credible alternative to linesearch and trust-region for smooth nonconvex optimization, with optimal complexity amongst second-order methods. Here we consider a general/new class of…
A cornerstone of geometric reconstruction, rotation averaging seeks the set of absolute rotations that optimally explains a set of measured relative orientations between them. In addition to being an integral part of bundle adjustment and…
Recovering a function from its integrals over circular cones recently gained significance because of its relevance to novel medical imaging technologies such emission tomography using Compton cameras. In this paper we investigate the case…
Influenced by the fact that vorticity represents rotation for rigid body, people believe it also works for fluid flow. However, the theoretical predictions by vorticity do not match experiment results, which drove scientists to look for…
Orbital Angular Momentum (OAM)-based communication systems offer high-capacity multiplexing in line-of-sight (LOS) scenarios; yet, their performance is sensitive to nodal misalignment, which disrupts modal orthogonality, hindering the data…
We report a real-space renormalization group (RSRG) algorithm, which is formulated through Baxter's corner transfer matrix (CTM), for two-dimensional (d = 2) classical lattice models. The new method performs the renormalization group…