期刊
INVERSE PROBLEMS
卷 28, 期 10, 页码 -出版社
IOP PUBLISHING LTD
DOI: 10.1088/0266-5611/28/10/104004
关键词
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资金
- German Research Foundation DFG [1023, CRC 755]
In this paper, we study a Tikhonov-type method for ill-posed nonlinear operator equations g(dagger) = F(u(dagger)), where g(dagger) is an integrable, non-negative function. We assume that data are drawn from a Poisson process with density tg(dagger), where t > 0 may be interpreted as an exposure time. Such problems occur in many photonic imaging applications including positron emission tomography, confocal fluorescence microscopy, astronomic observations and phase retrieval problems in optics. Our approach uses a Kullback-Leibler-type data fidelity functional and allows for general convex penalty terms. We prove convergence rates of the expectation of the reconstruction error under a variational source condition as t -> infinity both for an a priori and for a Lepskii-type parameter choice rule.
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