Boying Wu

Adaptive Perona–Malik Model Based on the Variable Exponent for Image Denoising

This paper introduces a class of adaptive Perona-Malik (PM) diffusion, which combines the PM equation with the heat equation. The PM equation provides a potential algorithm for image segmentation, noise removal, edge detection, and image enhancement. However, the defect of traditional PM model is tending to cause the staircase effect and create new features in the processed image. Utilizing the edge indicator as a variable exponent, we can adaptively control the diffusion mode, which alternates between PM diffusion and Gaussian smoothing in accordance with the image feature. Computer experiments indicate that the present algorithm is very efficient for edge detection and noise removal.

Error estimation for the reproducing kernel method to solve linear boundary value problems

In the previous works, the authors presented the reproducing kernel method(RKM) for solving various boundary value problems. However, an effective error estimation for this method has not yet been discussed. The aim of this paper is to fill this gap. In this paper, we shall give the error estimation for the reproducing kernel method to solve linear boundary value problems.

A Doubly Degenerate Diffusion Model Based on the Gray Level Indicator for Multiplicative Noise Removal

Multiplicative noise removal is a challenging task in image processing. Inspired by the impressive performance of nonlinear diffusion models in additive noise removal, we address this problem in the view of nonlinear diffusion equation theories rather than the traditional variation methods. We develop a nonlinear diffusion filter denoising framework, which considers not only the information of the gradient of the image, but also the information of gray levels of the image. Furthermore, under this framework, we propose a doubly degenerate diffusion model for multiplicative noise removal, which is analyzed with respect to some of its properties and behavior in denoising process. In numerical aspects, we present an efficient scheme which uses a stabilization by fast explicit diffusion for the implementation of the multiplicative noise removal model. Finally, the experimental results illustrate effectiveness and efficiency of the proposed model.

A new reproducing kernel method for variable order fractional boundary value problems for functional differential equations

Based on reproducing kernel theory, a numerical method is proposed for solving variable order fractional boundary value problems for functional differential equations. In the previous works, piecewise polynomial reproducing kernels were employed to solve fractional differential equations. However, the computational cost of fractional order operator acting on such kernel functions is high. In this paper, reproducing kernels with polynomial form will be constructed and applied to solve variable order fractional functional boundary value problems. The method can reduce computation cost and provide highly accurate global approximate solutions.

Some numerical algorithms for solving the highly oscillatory second-order initial value problems ☆

Abstract In this paper, some numerical algorithms (spectral collocation method, block spectral collocation method, boundary value method, block boundary value method, implicit Runge–Kutta method, diagonally implicit Runge–Kutta method and total variation diminishing Runge–Kutta method) are used to solve the highly oscillatory second-order initial value problems. We first derive these methods for the first-order initial value problems, and then extend these methods to the highly oscillatory nonlinear systems by matrix analysis methods. These new methods preserve the accuracy of the original methods and the main advantages of these new methods are low storage requirements and high efficiency. Extensive numerical results are presented to demonstrate the convergence properties of these methods.

Local existence and uniqueness of solutions of a degenerate parabolic system

This article deals with a degenerate parabolic system coupled with general nonlinear terms. Using the method of regularization and monotone iteration technique, we obtain the local existence of solutions to the Dirichlet initial boundary value problem. We also establish the uniqueness of the solution if the reaction terms satisfy the Lipschitz condition.

Galerkin-Chebyshev spectral method and block boundary value methods for two-dimensional semilinear parabolic equations

In this paper, we present a high-order accurate method for two-dimensional semilinear parabolic equations. The method is based on a Galerkin-Chebyshev spectral method for discretizing spatial derivatives and a block boundary value methods of fourth-order for temporal discretization. Our formulation has high-order accurate in both space and time. Optimal a priori error bound is derived in the weighted Lω2

A Total Variation Model Based on the Strictly Convex Modification for Image Denoising

L^{2}_{\omega }

Reproducing Kernel Method for Fractional Riccati Differential Equations

-norm for the semidiscrete formulation. Extensive numerical results are presented to demonstrate the convergence properties of the method.

Combining nonmonotone conic trust region and line search techniques for unconstrained optimization

We propose a strictly convex functional in which the regular term consists of the total variation term and an adaptive logarithm based convex modification term. We prove the existence and uniqueness of the minimizer for the proposed variational problem. The existence, uniqueness, and long-time behavior of the solution of the associated evolution system is also established. Finally, we present experimental results to illustrate the effectiveness of the model in noise reduction, and a comparison is made in relation to the more classical methods of the traditional total variation (TV), the Perona-Malik (PM), and the more recent D-α-PM method. Additional distinction from the other methods is that the parameters, for manual manipulation, in the proposed algorithm are reduced to basically only one.