Volumetric Data Reduction in a Compressed Sensing Framework

In this paper, we investigate compressed sensing principles to devise an in‐situ data reduction framework for visualization of volumetric datasets. We exploit the universality of the compressed sensing framework and show that the proposed method offers a refinable data reduction approach for volumet...

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Published in:	Computer graphics forum Vol. 33; no. 3; pp. 111 - 120
Main Authors:	Xu, X., Sakhaee, E., Entezari, A.
Format:	Journal Article
Language:	English
Published:	Oxford Blackwell Publishing Ltd 01.06.2014
Subjects:	Analysis Categories and Subject Descriptors (according to ACM CCS) Compressed Computer graphics Data reduction Detection Fourier analysis I.4.10 [Image Processing and Computer Vision]: Image Representation-Volumetric I.4.2 [Image Processing and Computer Vision]: Compression-Approximate methods I.4.5 [Image Processing and Computer Vision]: Reconstruction-Transform methods Image processing systems Reconstruction Representations Studies Visualization Volumetric analysis
ISSN:	0167-7055, 1467-8659
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Abstract	In this paper, we investigate compressed sensing principles to devise an in‐situ data reduction framework for visualization of volumetric datasets. We exploit the universality of the compressed sensing framework and show that the proposed method offers a refinable data reduction approach for volumetric datasets. The accurate reconstruction is obtained from partial Fourier measurements of the original data that are sensed without any prior knowledge of specific feature domains for the data. Our experiments demonstrate the superiority of surfacelets for efficient representation of volumetric data. Moreover, we establish that the accuracy of reconstruction can further improve once a more effective basis for a sparser representation of the data becomes available.
AbstractList	In this paper, we investigate compressed sensing principles to devise an in‐situ data reduction framework for visualization of volumetric datasets. We exploit the universality of the compressed sensing framework and show that the proposed method offers a refinable data reduction approach for volumetric datasets. The accurate reconstruction is obtained from partial Fourier measurements of the original data that are sensed without any prior knowledge of specific feature domains for the data. Our experiments demonstrate the superiority of surfacelets for efficient representation of volumetric data. Moreover, we establish that the accuracy of reconstruction can further improve once a more effective basis for a sparser representation of the data becomes available. In this paper, we investigate compressed sensing principles to devise an in-situ data reduction framework for visualization of volumetric datasets. We exploit the universality of the compressed sensing framework and show that the proposed method offers a refinable data reduction approach for volumetric datasets. The accurate reconstruction is obtained from partial Fourier measurements of the original data that are sensed without any prior knowledge of specific feature domains for the data. Our experiments demonstrate the superiority of surfacelets for efficient representation of volumetric data. Moreover, we establish that the accuracy of reconstruction can further improve once a more effective basis for a sparser representation of the data becomes available. [PUBLICATION ABSTRACT]
Author	Entezari, A. Xu, X. Sakhaee, E.
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Copyright	2014 The Author(s) Computer Graphics Forum © 2014 The Eurographics Association and John Wiley & Sons Ltd. Published by John Wiley & Sons Ltd. 2014 The Eurographics Association and John Wiley & Sons Ltd.
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References_xml	– reference: Ma K.: In situ visualization at extreme scale: Challenges and opportunities. Computer Graphics and Applications, IEEE 29, 6 (2009), 14-19. 2 – reference: Tropp J., Wright S.: Computational methods for sparse solution of linear inverse problems. Proceedings of the IEEE 98, 6 (2010), 948-958. 3, 4 – reference: Candès E., Romberg J., Tao T.: Robust uncertainty principles: exact signal, reconstruction from highly incomplete frequency information. IEEE Transactions on Information Theory 52, 2 (2006), 489-509. 3, 4 – reference: Duarte M., Davenport M., Takhar D., Laska J., Sun T., Kelly K., Baraniuk R.: Single-pixel imaging via compressive sampling. Signal Processing Magazine, IEEE 25, 2 (2008), 83-91. 1 – reference: Elad M.: Sparse and Redundant Representations - From Theory to Applications in Signal and Image Processing. Springer, 2010. 2 – reference: Hassanieh H., Indyk P., Katabi D., Price E.: Simple and practical algorithm for sparse fourier transform. In Proceedings of the Twenty-third Annual ACM-SIAM Symposium on Discrete Algorithms (2012), SODA '12, SIAM, pp. 1183-1194. 9 – reference: Unser M.: Sampling-50 Years after Shannon. Proceedings of the IEEE 88, 4 (April 2000), 569-587. 1 – reference: Baraniuk R.: More is less: Signal processing and the data deluge. Science 331, 6018 (2011), 717-719. 1 – reference: Candès E., Demanet L., Donoho D., Ying L.: Fast discrete curvelet transforms. Multiscale Modeling & Simulation 5, 3 (Jan. 2006), 861-899. 1, 4, 5 – reference: Pan X., Sidky E., Vannier M.: Why do commercial CT scanners still employ traditional, filtered back-projection for image reconstruction? Inverse Problems 25, 12 (2009), 123009. 1 – reference: Lustig M., Donoho D., Santos J., Pauly J.: Compressed sensing mri. Signal Processing Magazine, IEEE 25, 2 (march 2008), 72-82. 1 – reference: Lustig M., Donoho D., Pauly J.: Sparse mri: The application of compressed sensing for rapid mr imaging. Magnetic Resonance in Medicine 58, 6 (2007), 1182-1195. 1 – reference: Candès E., Tao T.: Decoding by linear programming. IEEE Transactions on Information Theory 51, 12 (2005). 3 – reference: Kutyniok G., Labate D.: Shearlets: Multiscale Analysis for Multivariate Data, first ed. Birkhauser Publication, 2012. 1, 4 – reference: Tropp J., Gilbert A.: Signal recovery from random measurements via orthogonal matching pursuit. IEEE Transactions on Information Theory 53, 12 (2007), 4655-4666. 3 – reference: Candès E., Romberg J., Tao T.: Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information. IEEE Transactions on Information Theory 52, 2 (2006), 489-509. 3 – reference: Donoho D.: Compressed sensing. IEEE Transactions on Information Theory 52, 4 (2006), 1289-1306. 3, 4 – reference: Candès E., Tao T.: Near-optimal signal recovery from random projections: Universal encoding strategies. IEEE Transactions on Information Theory 52, 12 (2006), 5406-5425. 3 – reference: Becker S., Bobin J., Candès E.: NESTA: A fast and accurate first-order method for sparse recovery. SIAM J. Imaging Sciences 4, 1 (2011), 1-39. 5 – reference: Franco J., BernabÃl' G., Fernãandez J., UjaldÃşn M.: Parallel 3d fast wavelet transform on many-core gpus and multicore cpus. Procedia Computer Science 1, 1 (2010), 1101-1110. 9 – reference: Chen S., Donoho D., Saunders M.: Atomic decomposition by basis pursuit. SIAM Journal on Scientific Computing 20, 1 (1998), 33-61. 3, 4 – reference: Gobbetti E., Guitián J. A. I., Marton F.: COVRA: A compression-domain output-sensitive volume rendering architecture based on a sparse representation of voxel blocks. Comput. Graph. 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Snippet	In this paper, we investigate compressed sensing principles to devise an in‐situ data reduction framework for visualization of volumetric datasets. We exploit... In this paper, we investigate compressed sensing principles to devise an in-situ data reduction framework for visualization of volumetric datasets. We exploit...
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SubjectTerms	Analysis Categories and Subject Descriptors (according to ACM CCS) Compressed Computer graphics Data reduction Detection Fourier analysis I.4.10 [Image Processing and Computer Vision]: Image Representation-Volumetric I.4.2 [Image Processing and Computer Vision]: Compression-Approximate methods I.4.5 [Image Processing and Computer Vision]: Reconstruction-Transform methods Image processing systems Reconstruction Representations Studies Visualization Volumetric analysis
Title	Volumetric Data Reduction in a Compressed Sensing Framework
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