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Compressive Image Reconstruction in Reduced Union of Subspaces
Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering. (Computer Graphics and Image Processing)
Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering. (Computer Graphics and Image Processing)
Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering. (Computer Graphics and Image Processing)ORCID iD: 0000-0002-7765-1747
2015 (English)In: Computer Graphics Forum, ISSN 1467-8659, Vol. 34, no 2, p. 33-44Article in journal (Refereed) Published
Abstract [en]

We present a new compressed sensing framework for reconstruction of incomplete and possibly noisy images and their higher dimensional variants, e.g. animations and light-fields. The algorithm relies on a learning-based basis representation. We train an ensemble of intrinsically two-dimensional (2D) dictionaries that operate locally on a set of 2D patches extracted from the input data. We show that one can convert the problem of 2D sparse signal recovery to an equivalent 1D form, enabling us to utilize a large family of sparse solvers. The proposed framework represents the input signals in a reduced union of subspaces model, while allowing sparsity in each subspace. Such a model leads to a much more sparse representation than widely used methods such as K-SVD. To evaluate our method, we apply it to three different scenarios where the signal dimensionality varies from 2D (images) to 3D (animations) and 4D (light-fields). We show that our method outperforms state-of-the-art algorithms in computer graphics and image processing literature.

Place, publisher, year, edition, pages
John Wiley & Sons Ltd , 2015. Vol. 34, no 2, p. 33-44
Keywords [en]
Image reconstruction, compressed sensing, light field imaging
National Category
Signal Processing
Identifiers
URN: urn:nbn:se:liu:diva-119639DOI: 10.1111/cgf.12539ISI: 000358326600008OAI: oai:DiVA.org:liu-119639DiVA, id: diva2:825377
Conference
Eurographics 2015
Projects
VPS
Funder
Swedish Foundation for Strategic Research , IIS11-0081Available from: 2015-06-23 Created: 2015-06-23 Last updated: 2018-11-23Bibliographically approved
In thesis
1. Sparse representation of visual data for compression and compressed sensing
Open this publication in new window or tab >>Sparse representation of visual data for compression and compressed sensing
2018 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The ongoing advances in computational photography have introduced a range of new imaging techniques for capturing multidimensional visual data such as light fields, BRDFs, BTFs, and more. A key challenge inherent to such imaging techniques is the large amount of high dimensional visual data that is produced, often requiring GBs, or even TBs, of storage. Moreover, the utilization of these datasets in real time applications poses many difficulties due to the large memory footprint. Furthermore, the acquisition of large-scale visual data is very challenging and expensive in most cases. This thesis makes several contributions with regards to acquisition, compression, and real time rendering of high dimensional visual data in computer graphics and imaging applications.

Contributions of this thesis reside on the strong foundation of sparse representations. Numerous applications are presented that utilize sparse representations for compression and compressed sensing of visual data. Specifically, we present a single sensor light field camera design, a compressive rendering method, a real time precomputed photorealistic rendering technique, light field (video) compression and real time rendering, compressive BRDF capture, and more. Another key contribution of this thesis is a general framework for compression and compressed sensing of visual data, regardless of the dimensionality. As a result, any type of discrete visual data with arbitrary dimensionality can be captured, compressed, and rendered in real time.

This thesis makes two theoretical contributions. In particular, uniqueness conditions for recovering a sparse signal under an ensemble of multidimensional dictionaries is presented. The theoretical results discussed here are useful for designing efficient capturing devices for multidimensional visual data. Moreover, we derive the probability of successful recovery of a noisy sparse signal using OMP, one of the most widely used algorithms for solving compressed sensing problems.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2018. p. 158
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1963
National Category
Media Engineering
Identifiers
urn:nbn:se:liu:diva-152863 (URN)10.3384/diss.diva-152863 (DOI)9789176851869 (ISBN)
Public defence
2018-12-14, Domteatern, Visualiseringscenter C, Kungsgatan 54, Campus Norrköping, Norrköping, 09:15 (English)
Opponent
Supervisors
Available from: 2018-11-23 Created: 2018-11-23 Last updated: 2018-11-23Bibliographically approved

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Miandji, EhsanKronander, JoelUnger, Jonas

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