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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

  • Vol. 20, Iss. 3 — Mar. 1, 2003
  • pp: 439–449

Relaxed ordered-subset algorithm for penalized-likelihood image restoration

Saowapak Sotthivirat and Jeffrey A. Fessler  »View Author Affiliations


JOSA A, Vol. 20, Issue 3, pp. 439-449 (2003)
http://dx.doi.org/10.1364/JOSAA.20.000439


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Abstract

The expectation-maximization (EM) algorithm for maximum-likelihood image recovery is guaranteed to converge, but it converges slowly. Its ordered-subset version (OS-EM) is used widely in tomographic image reconstruction because of its order-of-magnitude acceleration compared with the EM algorithm, but it does not guarantee convergence. Recently the ordered-subset, separable-paraboloidal-surrogate (OS-SPS) algorithm with relaxation has been shown to converge to the optimal point while providing fast convergence. We adapt the relaxed OS-SPS algorithm to the problem of image restoration. Because data acquisition in image restoration is different from that in tomography, we employ a different strategy for choosing subsets, using pixel locations rather than projection angles. Simulation results show that the relaxed OS-SPS algorithm can provide an order-of-magnitude acceleration over the EM algorithm for image restoration. This new algorithm now provides the speed and guaranteed convergence necessary for efficient image restoration.

© 2003 Optical Society of America

OCIS Codes
(100.0100) Image processing : Image processing
(100.1830) Image processing : Deconvolution
(100.2000) Image processing : Digital image processing
(100.3020) Image processing : Image reconstruction-restoration
(100.3190) Image processing : Inverse problems
(180.1790) Microscopy : Confocal microscopy

History
Original Manuscript: May 20, 2002
Revised Manuscript: October 14, 2002
Manuscript Accepted: October 15, 2002
Published: March 1, 2003

Citation
Saowapak Sotthivirat and Jeffrey A. Fessler, "Relaxed ordered-subset algorithm for penalized-likelihood image restoration," J. Opt. Soc. Am. A 20, 439-449 (2003)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-20-3-439

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