2015-11-01Zeitschriftenartikel DOI: 10.18452/13698
Bilevel Optimization for Calibrating Point Spread Functions in Blind Deconvolution
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 partic- ular imaging modality. Bilevel problems of such type are investigated system- atically. 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.
This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Inverse Problems and Imaging following peer review. The definitive publisher-authenticated version (Michael Hintermüller, Tao Wu;Bilevel optimization for calibrating point spread functions in blind deconvolution;Inverse Problems and Imaging;Pages: 1139 - 1169, Volume 9, Issue 4, November 2015 doi:10.3934/ipi.2015.9.1139 ) is available online at AIMS:http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=11746
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