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On Probability of Support Recovery for Orthogonal Matching Pursuit Using Mutual Coherence
Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering. (Computer Graphics and Image Processing)
Qualcomm Technologies Inc., San Jose, CA, USA.
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
Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI, USA. (Ultra high-speed Nonlinear Integrated Circuit (UNIC))
2017 (English)In: IEEE Signal Processing Letters, ISSN 1070-9908, E-ISSN 1558-2361, Vol. 24, no 11, p. 1646-1650Article in journal (Refereed) Published
Abstract [en]

In this paper we present a new coherence-based performance guarantee for the Orthogonal Matching Pursuit (OMP) algorithm. A lower bound for the probability of correctly identifying the support of a sparse signal with additive white Gaussian noise is derived. Compared to previous work, the new bound takes into account the signal parameters such as dynamic range, noise variance, and sparsity. Numerical simulations show significant improvements over previous work and a closer match to empirically obtained results of the OMP algorithm.

Place, publisher, year, edition, pages
IEEE Signal Processing Society, 2017. Vol. 24, no 11, p. 1646-1650
Keywords [en]
Compressed Sensing (CS), Sparse Recovery, Orthogonal Matching Pursuit (OMP), Mutual Coherence
National Category
Signal Processing
Identifiers
URN: urn:nbn:se:liu:diva-141613DOI: 10.1109/LSP.2017.2753939ISI: 000412501600001OAI: oai:DiVA.org:liu-141613DiVA, id: diva2:1146543
Available from: 2017-10-03 Created: 2017-10-03 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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Publisher's full texthttp://ieeexplore.ieee.org.e.bibl.liu.se/document/8039500/

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Miandji, EhsanUnger, Jonas

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