## Nonquadratic penalization improves near-infrared diffuse optical tomography |

JOSA A, Vol. 30, Issue 8, pp. 1516-1523 (2013)

http://dx.doi.org/10.1364/JOSAA.30.001516

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### Abstract

A new approach that can easily incorporate any generic penalty function into the diffuse optical tomographic image reconstruction is introduced to show the utility of nonquadratic penalty functions. The penalty functions that were used include quadratic (ℓ_{2}), absolute (ℓ_{1}), Cauchy, and Geman–McClure. The regularization parameter in each of these cases was obtained automatically by using the generalized cross-validation method. The reconstruction results were systematically compared with each other via utilization of quantitative metrics, such as relative error and Pearson correlation. The reconstruction results indicate that, while the quadratic penalty may be able to provide better separation between two closely spaced targets, its contrast recovery capability is limited, and the sparseness promoting penalties, such as ℓ_{1}, Cauchy, and Geman–McClure have better utility in reconstructing high-contrast and complex-shaped targets, with the Geman–McClure penalty being the most optimal one.

© 2013 Optical Society of America

**OCIS Codes**

(100.3010) Image processing : Image reconstruction techniques

(100.3190) Image processing : Inverse problems

(110.6960) Imaging systems : Tomography

(170.0170) Medical optics and biotechnology : Medical optics and biotechnology

(110.0113) Imaging systems : Imaging through turbid media

(110.6955) Imaging systems : Tomographic imaging

**ToC Category:**

Medical Optics and Biotechnology

**History**

Original Manuscript: March 20, 2013

Revised Manuscript: June 8, 2013

Manuscript Accepted: June 10, 2013

Published: July 15, 2013

**Virtual Issues**

Vol. 8, Iss. 9 *Virtual Journal for Biomedical Optics*

**Citation**

Ravi Prasad K. Jagannath and Phaneendra K. Yalavarthy, "Nonquadratic penalization improves near-infrared diffuse optical tomography," J. Opt. Soc. Am. A **30**, 1516-1523 (2013)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-30-8-1516

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