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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| JOSA A: OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Stephen A. Burns
  • Vol. 25, Iss. 5 — May. 1, 2008
  • pp: 1199–1214

Optics InfoBase > JOSA A > Volume 25 > Issue 5 > Page 1199

Sparsity constrained regularization for multiframe image restoration

Premchandra M. Shankar and Mark A. Neifeld

JOSA A, Vol. 25, Issue 5, pp. 1199-1214        doi:10.1364/JOSAA.25.001199

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  • OCIS Codes:
  • (100.6640) Image processing : Superresolution
  • (110.4155) Imaging systems : Multiframe image processing
ToC Category:
Image Processing

Citation
Premchandra M. Shankar and Mark A. Neifeld, "Sparsity constrained regularization for multiframe image restoration," J. Opt. Soc. Am. A 25, 1199-1214 (2008)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-25-5-1199

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Abstract

In this paper we present a new algorithm for restoring an object from multiple undersampled low-resolution (LR) images that are degraded by optical blur and additive white Gaussian noise. We formulate the multiframe superresolution problem as maximum a posteriori estimation. The prior knowledge that the object is sparse in some domain is incorporated in two ways: first we use the popular ℓ1 norm as the regularization operator. Second, we model wavelet coefficients of natural objects using generalized Gaussian densities. The model parameters are learned from a set of training objects, and the regularization operator is derived from these parameters. We compare the results from our algorithms with an expectation-maximization (EM) algorithm for ℓ1 norm minimization and also with the linear minimum-mean-squared error (LMMSE) estimator. Using only eight 4×4 pixel downsampled LR images the reconstruction errors of object estimates obtained from our algorithm are 5.5% smaller than by the EM method and 14.3% smaller than by the LMMSE method.

© 2008 Optical Society of America

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History
Original Manuscript: November 29, 2007
Manuscript Accepted: February 21, 2008
Published: April 30, 2008

References

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Author Affiliations

Premchandra M. Shankar, Mark A. Neifeld

Department of Electrical and Computer Engineering

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