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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. 4 — Apr. 1, 2014
  • pp: 852–862

Performance evaluation of typical approximation algorithms for nonconvex ℓp-minimization in diffuse optical tomography

Calvin B. Shaw and Phaneendra K. Yalavarthy  »View Author Affiliations


JOSA A, Vol. 31, Issue 4, pp. 852-862 (2014)
http://dx.doi.org/10.1364/JOSAA.31.000852


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Abstract

The sparse estimation methods that utilize the ℓp-norm, with p being between 0 and 1, have shown better utility in providing optimal solutions to the inverse problem in diffuse optical tomography. These ℓp-norm-based regularizations make the optimization function nonconvex, and algorithms that implement ℓp-norm minimization utilize approximations to the original ℓp-norm function. In this work, three such typical methods for implementing the ℓp-norm were considered, namely, iteratively reweighted ℓ1-minimization (IRL1), iteratively reweighted least squares (IRLS), and the iteratively thresholding method (ITM). These methods were deployed for performing diffuse optical tomographic image reconstruction, and a systematic comparison with the help of three numerical and gelatin phantom cases was executed. The results indicate that these three methods in the implementation of ℓp-minimization yields similar results, with IRL1 fairing marginally in cases considered here in terms of shape recovery and quantitative accuracy of the reconstructed diffuse optical tomographic images.

© 2014 Optical Society of America

OCIS Codes
(170.0110) Medical optics and biotechnology : Imaging systems
(170.3010) Medical optics and biotechnology : Image reconstruction techniques
(170.3660) Medical optics and biotechnology : Light propagation in tissues
(170.3880) Medical optics and biotechnology : Medical and biological imaging

ToC Category:
Medical Optics and Biotechnology

History
Original Manuscript: December 5, 2013
Revised Manuscript: February 19, 2014
Manuscript Accepted: February 19, 2014
Published: March 28, 2014

Virtual Issues
Vol. 9, Iss. 6 Virtual Journal for Biomedical Optics

Citation
Calvin B. Shaw and Phaneendra K. Yalavarthy, "Performance evaluation of typical approximation algorithms for nonconvex ℓp-minimization in diffuse optical tomography," J. Opt. Soc. Am. A 31, 852-862 (2014)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-31-4-852


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