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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Franco Gori
  • Vol. 31, Iss. 7 — Jul. 1, 2014
  • pp: 1369–1394

Compressed sampling strategies for tomography

Yan Kaganovsky, Daheng Li, Andrew Holmgren, HyungJu Jeon, Kenneth P. MacCabe, David G. Politte, Joseph A. O’Sullivan, Lawrence Carin, and David J. Brady  »View Author Affiliations


JOSA A, Vol. 31, Issue 7, pp. 1369-1394 (2014)
http://dx.doi.org/10.1364/JOSAA.31.001369


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Abstract

We investigate new sampling strategies for projection tomography, enabling one to employ fewer measurements than expected from classical sampling theory without significant loss of information. Inspired by compressed sensing, our approach is based on the understanding that many real objects are compressible in some known representation, implying that the number of degrees of freedom defining an object is often much smaller than the number of pixels/voxels. We propose a new approach based on quasi-random detector subsampling, whereas previous approaches only addressed subsampling with respect to source location (view angle). The performance of different sampling strategies is considered using object-independent figures of merit, and also based on reconstructions for specific objects, with synthetic and real data. The proposed approach can be implemented using a structured illumination of the interrogated object or the detector array by placing a coded aperture/mask at the source or detector side, respectively. Advantages of the proposed approach include (i) for structured illumination of the detector array, it leads to fewer detector pixels and allows one to integrate detectors for scattered radiation in the unused space; (ii) for structured illumination of the object, it leads to a reduced radiation dose for patients in medical scans; (iii) in the latter case, the blocking of rays reduces scattered radiation while keeping the same energy in the transmitted rays, resulting in a higher signal-to-noise ratio than that achieved by lowering exposure times or the energy of the source; (iv) compared to view-angle subsampling, it allows one to use fewer measurements for the same image quality, or leads to better image quality for the same number of measurements. The proposed approach can also be combined with view-angle subsampling.

© 2014 Optical Society of America

OCIS Codes
(110.6960) Imaging systems : Tomography
(110.7440) Imaging systems : X-ray imaging
(340.7430) X-ray optics : X-ray coded apertures
(340.7440) X-ray optics : X-ray imaging
(110.6955) Imaging systems : Tomographic imaging

ToC Category:
Imaging Systems

History
Original Manuscript: February 18, 2014
Revised Manuscript: April 19, 2014
Manuscript Accepted: April 20, 2014
Published: June 9, 2014

Citation
Yan Kaganovsky, Daheng Li, Andrew Holmgren, HyungJu Jeon, Kenneth P. MacCabe, David G. Politte, Joseph A. O’Sullivan, Lawrence Carin, and David J. Brady, "Compressed sampling strategies for tomography," J. Opt. Soc. Am. A 31, 1369-1394 (2014)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-31-7-1369

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