## Relaxed ordered-subset algorithm for penalized-likelihood image restoration

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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