The iteratively regularized Gauss-Newton method with convex constraints and applications in 4Pi microscopy
The iteratively regularized Gauss-Newton method with convex constraints and applications in 4Pi microscopy
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DOI：
10.1088/0266-5611/28/1/015012
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发表时间：
2012-01-01
期刊：
影响因子：
2.1
通讯作者：
Hohage, Thorsten
中科院分区：
文献类型：
--
作者：
Stueck, Robert;Burger, Martin;Hohage, Thorsten
本文研究了具有凸约束的非线性不适定算子方程的数值解法。我们研究了一种牛顿型方法，该方法包括在每个迭代步骤中将线性Tikhonov正则化与凸约束应用于牛顿方程。当算子和右端都有误差且所有误差水平趋于零时，分析了这种迭代正则化方法的收敛性。我们的研究一直是出于联合估计的对象和相位在4Pi显微镜，这导致了一个半盲反卷积问题的非负约束。所提出的算法的性能示出了模拟和三维实验数据。
This paper is concerned with the numerical solution of nonlinear ill-posed operator equations involving convex constraints. We study a Newton-type method which consists in applying linear Tikhonov regularization with convex constraints to the Newton equations in each iteration step. Convergence of this iterative regularization method is analyzed if both the operator and the right-hand side are given with errors and all error levels tend to zero. Our study has been motivated by the joint estimation of object and phase in 4Pi microscopy, which leads to a semi-blind deconvolution problem with nonnegativity constraints. The performance of the proposed algorithm is illustrated both for simulated and for three-dimensional experimental data.