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.
Abstract. In this paper we present two improved arithmetic-geometric inequalities with Kantorovich constant (Lemma 3 and Lemma 5), based on which we provide some refinements in the operator case and then finally refer to the operator inequalities involving Heinz and Heron means.Mathematics subject classification (2010): 15A45,15A60.
In this work, we propose a three-term derivative-free projection method to solve nonlinear monotone equations with convex constraints based on the structures of the famous Dai-Yuan (DY) conjugate gradient method and the three-term conjugate gradient method. The proposed derivative-free method is suitable for solving large-scale problems due to its simple structure and lower storage requirement. The search direction satisfies the sufficient descent property independent of any line search. The global convergence is established under some conditions. The preliminary numerical results indicate that the proposed method is robust and effective.
In the article, we establish a new Hermite-Hadamard type inequality for the coordinate convex function by constructing two monotonic sequences. The given result is the generalization and improvement of some previously obtained results.
ABSTRACT:We extend the range of the weighted operator means for v / ∈ [0, 1] and obtain some corresponding operator inequalities. We also present several reversed Young-type inequalities.
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