期刊
INVERSE PROBLEMS AND IMAGING
卷 9, 期 4, 页码 1139-1169出版社
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/ipi.2015.9.1139
关键词
Image processing; blind deconvolution; bilevel optimization; mathematical programs with equilibrium constraints; projected gradient method
资金
- Austrian Science Fund (FWF) through START-Project [Y305]
- Austrian Science Fund (FWF) through SFB-Project [F3204]
- German Research Foundation DFG [HI1466/7-1]
- Research Center MATHEON [C-5E15]
- Einstein Center for Mathematics Berlin
- Austrian Science Fund (FWF) [F 3204] Funding Source: researchfish
Blind deconvolution problems arise in many imaging modalities, where both the underlying point spread function, which parameterizes the convolution operator, and the source image need to be identified. In this work, a novel bilevel optimization approach to blind deconvolution is proposed. The lower-level problem refers to the minimization of a total-variation model, as is typically done in non-blind image deconvolution. The upper-level objective takes into account additional statistical information depending on the particular imaging modality. Bilevel problems of such type are investigated systematically. Analytical properties of the lower-level solution mapping are established based on Robinson's strong regularity condition. Furthermore, several stationarity conditions are derived from the variational geometry induced by the lower-level problem. Numerically, a projected-gradient-type method is employed to obtain a Clarke-type stationary point and its convergence properties are analyzed. We also implement an efficient version of the proposed algorithm and test it through the experiments on point spread function calibration and multiframe blind deconvolution.
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