Humboldt-Universität zu Berlin - Mathematisch-Naturwissenschaftliche Fakultät - Institut für Mathematik

Preprint 2014-25

Michael Hintermüller, Tao Wu


Bilevel Optimization for Calibrating Point Spread Functions in Blind Deconvolution


Abstract: 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 be identied. 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 condi-
tion. Furthermore, several stationarity conditions are derived from the variational geometry
induced by the lower-level problem. Numerically, a projected-gradient-type method is em-
ployed to obtain a Clarke-type stationary point and its convergence properties are analyzed.
We also implement an ecient version of the proposed algorithm and test it through the
experiments on point spread function calibration and multiframe blind deconvolution.


Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 2014-25


31 pp.