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Block-based Collaborative 3-D Transform Domain Modeling in Inverse Imaging

Research output: Book/ReportDoctoral thesisCollection of Articles

Details

Original languageEnglish
PublisherTampere University of Technology
Number of pages78
ISBN (Electronic)978-952-15-3214-6
ISBN (Print)978-952-15-3101-9
Publication statusPublished - 5 Aug 2013
Publication typeG5 Doctoral dissertation (article)

Publication series

NameTampere University of Technology. Publication
PublisherTampere University of Technology
Volume1145
ISSN (Print)1459-2045

Abstract

The recent developments in image and video denoising have brought a new generation of filtering algorithms achieving unprecedented restoration quality. This quality mainly follows from exploiting various features of natural images. The nonlocal self-similarity and sparsity of representations are key elements of the novel filtering algorithms, with the best performance achieved by adaptively aggregating multiple redundant and sparse estimates. In a very broad sense, the filters are now able, given a perturbed image, to identify its plausible representative in the space or manifold of possible solutions. Thus, they are powerful tools not only for noise removal, but also for providing accurate adaptive regularization to many ill-conditioned inverse imaging problems. In this thesis we show how the image modeling of the well-known Block-matching 3-D transform domain (BM3D) filter can be exploited for designing efficient algorithms for image reconstruction. First, we formalize the BM3D-modeling in terms of the overcomplete sparse frame representation. We construct analysis and synthesis BM3D-frames and study their properties, making BM3D-modeling available for use in variational formulations of image reconstruction problems. Second, we demonstrate that standard variational formulations based on single objective optimization, such as Basis Pursuit Denoising and its various extensions, cannot be used with the imaging models generating non-tight frames, such as BM3D. We propose an alternative sparsity promoting problem formulation based on the generalized Nash equilibrium (GNE). Finally, using BM3D-frames we develop practical algorithms for image deblurring and super-resolution problems. To the best of our knowledge, these algorithms provide results which are the state of the art in the field.

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