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Sparse representation of visual data for compression and compressed sensing
Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.
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: urn:nbn:se:liu:diva-152863DOI: 10.3384/diss.diva-152863ISBN: 9789176851869 (print)OAI: oai:DiVA.org:liu-152863DiVA, id: diva2:1265420
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
List of papers
1. OMP-based DOA estimation performance analysis
Open this publication in new window or tab >>OMP-based DOA estimation performance analysis
2018 (English)In: Digital signal processing (Print), ISSN 1051-2004, E-ISSN 1095-4333, Vol. 79, p. 57-65Article in journal (Refereed) Published
Abstract [en]

In this paper, we present a new performance guarantee for Orthogonal Matching Pursuit (OMP) in the context of the Direction Of Arrival (DOA) estimation problem. For the first time, the effect of parameters such as sensor array configuration, as well as signal to noise ratio and dynamic range of the sources is thoroughly analyzed. In particular, we formulate a lower bound for the probability of detection and an upper bound for the estimation error. The proposed performance guarantee is further developed to include the estimation error as a user-defined parameter for the probability of detection. Numerical results show acceptable correlation between theoretical and empirical simulations. (C) 2018 Elsevier Inc. All rights reserved.

Place, publisher, year, edition, pages
ACADEMIC PRESS INC ELSEVIER SCIENCE, 2018
Keywords
Direction of arrival; Orthogonal Matching Pursuit (OMP); Mutual coherence; Array configuration
National Category
Signal Processing
Identifiers
urn:nbn:se:liu:diva-149841 (URN)10.1016/j.dsp.2018.04.006 (DOI)000437386200006 ()
Available from: 2018-08-02 Created: 2018-08-02 Last updated: 2018-11-23
2. On Probability of Support Recovery for Orthogonal Matching Pursuit Using Mutual Coherence
Open this publication in new window or tab >>On Probability of Support Recovery for Orthogonal Matching Pursuit Using Mutual Coherence
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
Keywords
Compressed Sensing (CS), Sparse Recovery, Orthogonal Matching Pursuit (OMP), Mutual Coherence
National Category
Signal Processing
Identifiers
urn:nbn:se:liu:diva-141613 (URN)10.1109/LSP.2017.2753939 (DOI)000412501600001 ()
Available from: 2017-10-03 Created: 2017-10-03 Last updated: 2018-11-23Bibliographically approved
3. ON NONLOCAL IMAGE COMPLETION USING AN ENSEMBLE OF DICTIONARIES
Open this publication in new window or tab >>ON NONLOCAL IMAGE COMPLETION USING AN ENSEMBLE OF DICTIONARIES
2016 (English)In: 2016 IEEE INTERNATIONAL CONFERENCE ON IMAGE PROCESSING (ICIP), IEEE , 2016, p. 2519-2523Conference paper, Published paper (Refereed)
Abstract [en]

In this paper we consider the problem of nonlocal image completion from random measurements and using an ensemble of dictionaries. Utilizing recent advances in the field of compressed sensing, we derive conditions under which one can uniquely recover an incomplete image with overwhelming probability. The theoretical results are complemented by numerical simulations using various ensembles of analytical and training-based dictionaries.

Place, publisher, year, edition, pages
IEEE, 2016
Series
IEEE International Conference on Image Processing ICIP, ISSN 1522-4880
Keywords
compressed sensing; image completion; nonlocal; inverse problems; uniqueness conditions
National Category
Computer Vision and Robotics (Autonomous Systems)
Identifiers
urn:nbn:se:liu:diva-134107 (URN)10.1109/ICIP.2016.7532813 (DOI)000390782002114 ()978-1-4673-9961-6 (ISBN)
Conference
23rd IEEE International Conference on Image Processing (ICIP)
Available from: 2017-01-22 Created: 2017-01-22 Last updated: 2018-11-23
4. Compressive Image Reconstruction in Reduced Union of Subspaces
Open this publication in new window or tab >>Compressive Image Reconstruction in Reduced Union of Subspaces
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
Keywords
Image reconstruction, compressed sensing, light field imaging
National Category
Signal Processing
Identifiers
urn:nbn:se:liu:diva-119639 (URN)10.1111/cgf.12539 (DOI)000358326600008 ()
Conference
Eurographics 2015
Projects
VPS
Funder
Swedish Foundation for Strategic Research , IIS11-0081
Available from: 2015-06-23 Created: 2015-06-23 Last updated: 2018-11-23Bibliographically approved
5. Learning Based Compression of Surface Light Fields for Real-time Rendering of Global Illumination Scenes
Open this publication in new window or tab >>Learning Based Compression of Surface Light Fields for Real-time Rendering of Global Illumination Scenes
2013 (English)In: Proceedings of ACM SIGGRAPH ASIA 2013, ACM Press, 2013Conference paper, Published paper (Refereed)
Abstract [en]

We present an algorithm for compression and real-time rendering of surface light fields (SLF) encoding the visual appearance of objects in static scenes with high frequency variations. We apply a non-local clustering in order to exploit spatial coherence in the SLFdata. To efficiently encode the data in each cluster, we introducea learning based approach, Clustered Exemplar Orthogonal Bases(CEOB), which trains a compact dictionary of orthogonal basispairs, enabling efficient sparse projection of the SLF data. In ad-dition, we discuss the application of the traditional Clustered Principal Component Analysis (CPCA) on SLF data, and show that inmost cases, CEOB outperforms CPCA, K-SVD and spherical harmonics in terms of memory footprint, rendering performance andreconstruction quality. Our method enables efficient reconstructionand real-time rendering of scenes with complex materials and lightsources, not possible to render in real-time using previous methods.

Place, publisher, year, edition, pages
ACM Press, 2013
Keywords
computer graphics, global illumination, real-time, machine learning
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-99433 (URN)10.1145/2542355.2542385 (DOI)978-1-4503-2629-2 (ISBN)
Conference
SIGGRAPH Asia, 19-22 November 2013, Hong Kong
Projects
VPS
Funder
Swedish Foundation for Strategic Research , IIS11-0081Swedish Research Council
Available from: 2013-10-17 Created: 2013-10-17 Last updated: 2018-11-23Bibliographically approved

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Miandji, Ehsan

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