scholarly journals Solving Adaptive Image Restoration Problems via a Modified Projection Algorithm

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Hao Yang ◽  
Xueping Luo ◽  
Leiting Chen
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Image Restoration ◽  
Image Denoising ◽  
Existence And Uniqueness ◽  
Experimental Results ◽  
Projection Algorithm ◽  
Tv Regularization ◽  
Uniqueness Of The Solution ◽  
Quasi Variational Inequality

We introduce a new general TV regularizer, namely, generalized TV regularization, to study image denoising and nonblind image deblurring problems. In order to discuss the generalized TV image restoration with solution-driven adaptivity, we consider the existence and uniqueness of the solution for mixed quasi-variational inequality. Moreover, the convergence of a modified projection algorithm for solving mixed quasi-variational inequalities is also shown. The corresponding experimental results support our theoretical findings.

Variational model of sandpile growth

1996 ◽  
Vol 7 (3) ◽  
pp. 225-235 ◽  
Author(s):  
Leonid Prigozhin
Keyword(s):  
Variational Inequality ◽  
Existence And Uniqueness ◽  
Variational Model ◽  
Support Surface ◽  
Uniqueness Of The Solution ◽  
Quasi Variational Inequality ◽  
Steep Slopes

A model describing the evolving shape of a growing pile is considered, and is shown to be equivalent to an evolutionary quasi-variational inequality. If the support surface has no steep slopes, the inequality becomes a variational one. For this case existence and uniqueness of the solution are proved.

scholarly journals An Alternative Variational Framework for Image Denoising

2014 ◽  
Vol 2014 ◽  
pp. 1-16 ◽  
Author(s):  
Elisha Achieng Ogada ◽  
Zhichang Guo ◽  
Boying Wu
Keyword(s):  
Evolution Equation ◽  
Variational Problem ◽  
Image Restoration ◽  
Image Denoising ◽  
Total Variation ◽  
Existence And Uniqueness ◽  
Alternative Framework ◽  
Variational Framework ◽  
Uniqueness Of The Solution ◽  
Functional Coefficient

We propose an alternative framework for total variation based image denoising models. The model is based on the minimization of the total variation with a functional coefficient, where, in this case, the functional coefficient is a function of the magnitude of image gradient. We determine the considerations to bear on the choice of the functional coefficient. With the use of an example functional, we demonstrate the effectiveness of a model chosen based on the proposed consideration. In addition, for the illustrative model, we prove the existence and uniqueness of the minimizer of the variational problem. The existence and uniqueness of the solution associated evolution equation are also established. Experimental results are included to demonstrate the effectiveness of the selected model in image restoration over the traditional methods of Perona-Malik (PM), total variation (TV), and the D-α-PM method.

scholarly journals On the Bean critical-state model in superconductivity

1996 ◽  
Vol 7 (3) ◽  
pp. 237-247 ◽  
Author(s):  
L. Prigozhin
Keyword(s):  
Variational Inequalities ◽  
Critical State ◽  
Existence And Uniqueness ◽  
Critical State Model ◽  
Type Ii ◽  
Two Dimensional ◽  
Axially Symmetric ◽  
Uniqueness Of The Solution ◽  
Type Ii Superconductivity ◽  
Special Case

We consider two-dimensional and axially symmetric critical-state problems in type-II superconductivity, and show that these problems are equivalent to evolutionary quasi-variational inequalities. In a special case, where the inequalities become variational, the existence and uniqueness of the solution are proved.

scholarly journals Some New Classes of Extended General Mixed Quasi-Variational Inequalities

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Muhammad Aslam Noor ◽  
Khalida Inayat Noor
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Auxiliary Principle ◽  
Existence Of A Solution ◽  
Auxiliary Principle Technique ◽  
New Class ◽  
Special Cases ◽  
Quasi Variational Inequality

We consider and study a new class of variational inequality, which is called the extended general mixed quas-variational inequality. We use the auxiliary principle technique to study the existence of a solution of the extended general mixed quasi-variational inequality. Several special cases are also discussed. Results proved in this paper may stimulate further research in this area.

scholarly journals Certain remarks on a class of evolution quasi-variational inequalities

2000 ◽  
Vol 24 (12) ◽  
pp. 851-855 ◽  
Author(s):  
A. H. Siddiqi ◽  
Pammy Manchanda
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Existence Theorems ◽  
Static Problem ◽  
The Other ◽  
Time Dependent ◽  
Isotropic Hardening ◽  
Quasi Variational Inequality

We prove two existence theorems, one for evolution quasi-variational inequalities and the other for a time-dependent quasi-variational inequality modeling the quasi-static problem of elastoplasticity with combined kinetic-isotropic hardening.

scholarly journals Triple Hierarchical Variational Inequalities with Constraints of Mixed Equilibria, Variational Inequalities, Convex Minimization, and Hierarchical Fixed Point Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-25
Author(s):  
Lu-Chuan Ceng ◽  
Cheng-Wen Liao ◽  
Chin-Tzong Pang ◽  
Ching-Feng Wen
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Variational Inequalities ◽  
Convex Minimization ◽  
Solution Set ◽  
Projection Algorithm ◽  
Common Element ◽  
Point Problem ◽  
Hierarchical Fixed Point ◽  
Mixed Equilibria

We introduce and analyze a hybrid iterative algorithm by virtue of Korpelevich's extragradient method, viscosity approximation method, hybrid steepest-descent method, and averaged mapping approach to the gradient-projection algorithm. It is proven that under appropriate assumptions, the proposed algorithm converges strongly to a common element of the fixed point set of infinitely many nonexpansive mappings, the solution set of finitely many generalized mixed equilibrium problems (GMEPs), the solution set of finitely many variational inequality problems (VIPs), the solution set of general system of variational inequalities (GSVI), and the set of minimizers of convex minimization problem (CMP), which is just a unique solution of a triple hierarchical variational inequality (THVI) in a real Hilbert space. In addition, we also consider the application of the proposed algorithm to solve a hierarchical fixed point problem with constraints of finitely many GMEPs, finitely many VIPs, GSVI, and CMP. The results obtained in this paper improve and extend the corresponding results announced by many others.

scholarly journals The Maximum Norm Analysis of Schwarz Method for Elliptic Quasi-Variational Inequalities

2021 ◽  
Vol 45 (4) ◽  
pp. 635-645
Author(s):  
MOHAMMED BEGGAS ◽  
◽  
MOHAMMED HAIOUR ◽  
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Maximum Norm ◽  
Schwarz Method ◽  
Quasi Variational Inequality

In this paper, we present a maximum norm analysis of an overlapping Schwartz method on non matching grids for a quasi-variational inequality, where the obstacle and the second member depend on the solution. Our result improves and generalizes some previous results.

scholarly journals Existence of a solution of the quasi-variational inequality with semicontinuous operator

2006 ◽  
Vol 16 (2) ◽  
pp. 147-152
Author(s):  
Djurica Jovanov
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Existence Of A Solution ◽  
Feasible Set ◽  
Quasi Variational Inequality

The paper considers quasi-variational inequalities with point to set operator. The existence of a solution, in the case when the operator of the quasi-variational inequality is semi-continuous and the feasible set is convex and compact, is proved.

VALUATION OF EUROPEAN INSTALLMENT PUT OPTION: VARIATIONAL INEQUALITY APPROACH

2009 ◽  
Vol 11 (02) ◽  
pp. 279-307 ◽  
Author(s):  
ZHOU YANG ◽  
FAHUAI YI
Keyword(s):  
Variational Inequality ◽  
Free Boundary ◽  
Existence And Uniqueness ◽  
Parabolic Variational Inequality ◽  
Numerical Result ◽  
Put Option ◽  
Uniqueness Of The Solution

In this paper, we consider a parabolic variational inequality arising from the valuation of European installment put option. We prove the existence and uniqueness of the solution to the problem. Moreover, we obtain C∞ regularity and the bounds of the free boundary. Eventually, we show its numerical result by the binomial method.

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