MOROZOV'S DISCREPANCY PRINCIPLE FOR TIKHONOV-REGULARIZATION OF NONLINEAR OPERATORS
MOROZOV'S DISCREPANCY PRINCIPLE FOR TIKHONOV-REGULARIZATION OF NONLINEAR OPERATORS
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吉洪诺夫莫罗佐夫差异原理-非线性算子正则化
DOI：
10.1081/nfa-120003676
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发表时间：
2002
影响因子：
1.2
通讯作者：
R. Ramlau
中科院分区：
文献类型：
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作者：
R. Ramlau
摘要 我们考虑非线性算子方程的吉洪诺夫正则化的莫罗佐夫差异原理。结果表明，对算子 F 和方程的解 x* 进行较小的限制就已经保证了正则化参数 α 的存在，并且给出了收敛速度结果。最后，我们研究了一些实际相关的例子，例如医学成像（单光子发射计算机断层扫描）。说明了一大类非线性算子一般都会满足F上引入的条件。
ABSTRACT We consider Morozov's discrepancy principle for Tikhonov-regularization of nonlinear operator equations. It is shown that minor restrictions to the operator F and the solution x* of the equation already guarantee the existence of a regularization parameter α such that holds, and a convergence rate result is given. Finally we investigate some practically relevant examples, e.g., medical imaging (Single Photon Emission Computed Tomography). It is illustrated that the introduced conditions on F will be met in general by a large class of nonlinear operators.