Image denoising is a typical inverse problem and is hard to be solved. Fortunately, a powerful two-phase method for restoring images corrupted by high-level impulse noise has been proposed. The key point of the method is the computational efficiency of the second phase which requires the minimization of a smooth objective function defined on the terms of edge-preserving potential function. In this paper, we propose an effective three-term conjugate gradient method to restore the corrupted images in the second phase of two-phase method. An attractive feature of the proposed method is that the search direction satisfies the sufficient descent property at each iteration without any line search. The global convergence is established for general smooth functions under the Armijo-type line search. Preliminary numerical results are reported to indicate that the proposed method to be used for impulse noise removal is promising.
The variational iteration method (VIM) is applied to solve singular perturbation initial value problems with delays (SPIVPDs). Some convergence results of VIM for solving SPIVPDs are given. The obtained sequence of iterates is based on the use of general Lagrange multipliers; the multipliers in the functionals can be identified by the variational theory. Moreover, the numerical examples show the efficiency of the method.
Variational iteration method is applied to solve a class of delay differentialalgebraic equations. The obtained sequence of iteration is based on the use of Lagrange multipliers. The corresponding convergence results are obtained and successfully confirmed by some numerical examples.
This paper extends the continuous-time waveform relaxation method to singular perturbation initial value problems. The sufficient conditions for convergence of continuous-time waveform relaxation methods for singular perturbation initial value problems are given.
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