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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 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)
Based on some previous work about the connection between image restoration and fluid dynamics, we apply a two-step algorithm for image denoising. In the first step, we use a splitting scheme to study a nonlinear Stokes equation so that tangent vectors are obtained. We propose a continuous boundary condition in this paper. In the second step, we reconstruct(More)
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