A Kaczmarz Version of the REGINN-Landweber Iteration for Ill-Posed Problems in Banach Spaces
A Kaczmarz Version of the REGINN-Landweber Iteration for Ill-Posed Problems in Banach Spaces
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DOI：
10.1137/130923956
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发表时间：
2014-06
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影响因子：
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通讯作者：
F. Margotti;A. Rieder;A. Leitão
中科院分区：
文献类型：
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作者：
F. Margotti;A. Rieder;A. Leitão
本文提出并分析了求解Banach空间中非线性不适定问题的正则化迭代格式REGINN-Landweber的Kaczmarz形式[Q. Jin，Inverse Problems 28（2012），065002]. Kaczmarz方法被设计用于分裂成更小的子问题，然后在每个迭代步骤中循环处理的问题。在标准的假设下的Banach空间和非线性，我们证明了稳定性和（范数）收敛的噪声水平趋于零。此外，我们测试我们的计划上的二维电阻抗断层成像的反问题，不仅要说明我们的理论研究结果，但也研究不同的Banach空间上的重建电导率的影响。
In this work we present and analyze a Kaczmarz version of the iterative regularization scheme REGINN-Landweber for nonlinear ill-posed problems in Banach spaces [Q. Jin, Inverse Problems 28 (2012), 065002]. Kaczmarz methods are designed for problems which split into smaller subproblems which are then processed cyclically during each iteration step. Under standard assumptions on the Banach space and on the nonlinearity we prove stability and (norm) convergence as the noise level tends to zero. Further, we test our scheme on the inverse problem of two dimensional electric impedance tomography not only to illustrate our theoretical findings but also to study the influence of different Banach spaces on the reconstructed conductivities.