Sep 2026· Journal of Mathematical Study· 0 citations· 10 references
TL;DR
An effective hybrid regularization method is used to solve the Tikhonov regularization problem and design the regularization operator through an adaptive diagonal weighting matrix so that it has the effect of image restoration and edge preservation at the same time.
Abstract
We propose an algorithm based on iteratively reweighted norm strategy for image edge preservation. In order to achieve the purpose of boundary enhancement, we obtain a regularization operator through an adaptive process in the outer iteration and derive a Tikhonov regularization problem. An effective hybrid regularization method is used to solve this problem. The key to this method is to design the regularization operator through an adaptive diagonal weighting matrix so that it has the effect of image restoration and edge preservation at the same time. Numerical experiments are presented to demonstrate the feasibility and effectiveness of the algorithm.
A new phase field model for image decomposition and smoothing based on a modification of the Cahn-Hilliard equation which allows only the decomposition of phase values into multiple layers.
Acar Ruyam· Balkan Journal of Electrical...· 0 citations
This work proposes a variant of MM-GKS that alternately compresses and expands the search space while maintaining strict monotonic convergence, and shows that the method provably converges to the minimum of the selected functional, even if the search space dimension is kept very small.
Mirjeta Pasha, E. de Sturler, M. Kilmer· 0 citations
The total variation nonlocal (TV-nonlocal) model integrates several advanced features, including geometric active contours, anisotropic diffusion, regularization, and nonlocal gradients, demonstrating solid mathematical foundations. It achieves remarkable performance and interpretability when processing blurred edge se...
Guo-Liang He, Liu Yang· Computational and Applied Ma...· 0 citations
Abstract.
We propose a variational framework for joint removal of blur and multiplicative noise. While geometric priors effectively capture intrinsic image structure, relying on a single prior often introduces characteristic artifacts. Motivated by the geometric relationship between mean curvature and surface area, an...
Sheng-Kun Yang, Zhi-Chang Guo, Yao Li et al.· SIAM Journal of Imaging Scie...· 0 citations
We introduce the complex regularization method (CRM) which is a novel regularization method for radial basis function (RBF) interpolation problems. The proposed technique resolves rank–deficiency in such problems. It thus renders the need for supplementary polynomial terms to achieve invertibility across various RBFs u...
Lei-Hsin Kuo, C.-S. Chen, A. Karageorghis· Advances in Applied Mathemat...· 0 citations
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