Variational multiframe restoration of images degraded by noisy (stochastic) blur kernels

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Abstract

This article introduces and explores a class of degradation models in which an image is blurred by a noisy (stochastic) point spread function (PSF). The aim is to restore a sharper and cleaner image from the degraded one. Due to the highly ill-posed nature of the problem, we propose to recover the image given a sequence of several observed degraded images or multiframes. Thus we adopt the idea of the multiframe approach introduced for image super-resolution, which reduces distortions appearing in the degraded images. Moreover, we formulate variational minimization problems with the robust (local or nonlocal) L1 edge-preserving regularizing energy functionals, unlike prior works dealing with stochastic point spread functions. Several experimental results on grey-scale/color images and on real static video data are shown, illustrating that the proposed methods produce satisfactory results. We also apply the degradation model to a segmentation problem with simultaneous image restoration.

Keywords

Image restoration
Noisy blur kernel
Variational model
Total variation
Nonlocal method
Multiframe model

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Research supported by the National Science Foundation Grant DMS-0714945, the Center for Domain-Specific Computing (CDSC) under the NSF Expeditions in Computing Award CCF-0926127, a UCLA Faculty Research Grant 2009-2010, and the Spanish Government Agency Grant MINECO MTM2011-28043.