Xuecheng Tai

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A convergence proof is given for an abstract parabolic equation using general space decomposition techniques. The space decomposition technique may be a domain decomposition method, a multilevel method, or a multigrid method. It is shown that if the Euler or Crank-Nicolson scheme is used for the parabolic equation, then by suitably choosing the space(More)
This work presents some space decomposition algorithms for a convex minimization problem. The algorithms has linear rate of convergence and the rate of convergence depends only on four constants. The space decomposition could be a multigrid or domain decomposition method. We explain the detailed procedure to implement our algorithms for a two-level(More)
A large number of applications in image processing and computer vision depend on image quality. In this paper, main concerns are image denoising and deblurring simultaneously in a restoration task by three types of methodologies: non-convex regularization, inverse diffusion and shock filter. We discuss their relations in the context of image deblurring: the(More)
The standard approach for image reconstruction is to stabilize the problem by including an edge-preserving roughness penalty in addition to faithfulness to the data. However, this methodology produces noisy object boundaries and creates a staircase effect. State-of-the-art methods to correct these undesirable effects either have weak convergence guarantees(More)
In this paper, a new stable nonconforming mixed finite element scheme is proposed for the stationary conduction-convection problem, in which a new low order Crouzeix-Raviart type nonconforming rectangular element is taken as approximation space for the velocity, the piecewise constant element for the pressure and the bilinear element for the temperature,(More)
In this paper, we deal with l0-norm data fitting and total variation regularization for image compression and denoising. The l0-norm data fitting is used for measuring the number of non-zero wavelet coefficients to be employed to represent an image. The regularization term given by the total variation is to recover image edges. Due to intensive numerical(More)
Based on some previous work on the connection between image restoration and fluid dynamics, we apply a two-step algorithm for image denoising. In the first step, using a splitting scheme to study a nonlinear Stokes equation, tangent vectors are obtained. In the second step, an image is restored to fit the constructed tangent directions. We apply a fixed(More)
In the paper, we present an algorithm framework for the more general problem of minimizing the sum f(x) + ψ(x), where f is smooth and ψ is convex, but possible nonsmooth. At each step, the search direction of the algorithm is obtained by solving an optimization problem involving a quadratic term with diagonal Hessian and Barzilai-Borwein steplength plus(More)
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