Regularization of inverse problems by two-point gradient methods with convex constraints
Regularization of inverse problems by two-point gradient methods with convex constraints
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发表时间：
2018-12
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通讯作者：
M. Zhong;Wei Wang;Q. Jin
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作者：
M. Zhong;Wei Wang;Q. Jin
本文提出并分析了一种基于Landweber迭代和外推策略的求解Banach空间反问题的两点梯度法。该方法允许使用非光滑罚项，包括L^1和全变分类罚泛函，这在实际应用中重构解的稀疏性和分段恒定性等特殊特征方面具有重要意义。该方法的设计涉及的步长和组合参数的选择，仔细讨论。数值仿真结果验证了该方法的有效性。
In this paper, we propose and analyze a two-point gradient method for solving inverse problems in Banach spaces which is based on the Landweber iteration and an extrapolation strategy. The method allows to use non-smooth penalty terms, including the L^1 and the total variation-like penalty functionals, which are significant in reconstructing special features of solutions such as sparsity and piecewise constancy in practical applications. The design of the method involves the choices of the step sizes and the combination parameters which are carefully discussed. Numerical simulations are presented to illustrate the effectiveness of the proposed method.