An accelerated homotopy perturbation iteration for nonlinear ill-posed problems in Banach spaces with uniformly convex penalty
An accelerated homotopy perturbation iteration for nonlinear ill-posed problems in Banach spaces with uniformly convex penalty
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DOI：
10.1088/1361-6420/ac1ac2
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发表时间：
2021
期刊：
影响因子：
2.1
通讯作者：
Yuxin Xia;B. Han;Zhenwu Fu
中科院分区：
文献类型：
--
作者：
Yuxin Xia;B. Han;Zhenwu Fu
针对Banach空间中的非线性反问题，提出并分析了一种基于Nester ov策略的加速同伦摄动迭代算法。该方法允许使用类L 1和类全变分的惩罚项。因此，它可以处理所求解是稀疏的和分段恒定的情况。在一定的标准假设下，我们证明了该方法的收敛和正则化性质。数值实验表明了该方法的有效性和加速效果。
We propose and analyze an accelerated homotopy perturbation iteration based on Nesterov strategy for nonlinear inverse problems in Banach spaces. The method allows to use L 1-like and total variation-like penalty terms. Therefore, it can cope with the situation where the sought solution is sparse and piece-wise constant. Under some standard assumptions, we show the convergence and regularization properties of the method. Numerical experiments are presented to show the effectiveness as well as the acceleration effect of the proposed method.