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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 24 — Nov. 22, 2010
  • pp: 25306–25320

SVD for imaging systems with discrete rotational symmetry

Eric Clarkson, Robin Palit, and Mathew A. Kupinski  »View Author Affiliations

Optics Express, Vol. 18, Issue 24, pp. 25306-25320 (2010)

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The singular value decomposition (SVD) of an imaging system is a computationally intensive calculation for tomographic imaging systems due to the large dimensionality of the system matrix. The computation often involves memory and storage requirements beyond those available to most end users. We have developed a method that reduces the dimension of the SVD problem towards the goal of making the calculation tractable for a standard desktop computer. In the presence of discrete rotational symmetry we show that the dimension of the SVD computation can be reduced by a factor equal to the number of collection angles for the tomographic system. In this paper we present the mathematical theory for our method, validate that our method produces the same results as standard SVD analysis, and finally apply our technique to the sensitivity matrix for a clinical CT system. The ability to compute the full singular value spectra and singular vectors could augment future work in system characterization, image-quality assessment and reconstruction techniques for tomographic imaging systems.

© 2010 Optical Society of America

OCIS Codes
(110.2960) Imaging systems : Image analysis
(110.3000) Imaging systems : Image quality assessment
(110.6955) Imaging systems : Tomographic imaging

ToC Category:
Imaging Systems

Original Manuscript: August 13, 2010
Revised Manuscript: November 11, 2010
Manuscript Accepted: November 11, 2010
Published: November 19, 2010

Eric Clarkson, Robin Palit, and Matthew A. Kupinski, "SVD for imaging systems with discrete rotational symmetry," Opt. Express 18, 25306-25320 (2010)

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