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Optics Letters

| RAPID, SHORT PUBLICATIONS ON THE LATEST IN OPTICAL DISCOVERIES

  • Vol. 29, Iss. 5 — Mar. 1, 2004
  • pp: 504–506

Half-quadratic cost functions for phase unwrapping

Mariano Rivera and Jose L. Marroquin  »View Author Affiliations


Optics Letters, Vol. 29, Issue 5, pp. 504-506 (2004)
http://dx.doi.org/10.1364/OL.29.000504


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Abstract

We present a generic regularized formulation, based on robust half-quadratic regularization, for unwrapping noisy and discontinuous wrapped phase maps. Two cases are presented: the convex case and the nonconvex case. The unwrapped phase with the convex formulation is unique and robust to noise; however, the convex function solution deteriorates as a result of real discontinuities in phase maps. Therefore we also present a nonconvex formulation that, with a parameter continuation strategy, shows superior performance.

© 2004 Optical Society of America

OCIS Codes
(100.2650) Image processing : Fringe analysis
(100.3020) Image processing : Image reconstruction-restoration
(100.3190) Image processing : Inverse problems
(100.5070) Image processing : Phase retrieval
(120.5050) Instrumentation, measurement, and metrology : Phase measurement

Citation
Mariano Rivera and Jose L. Marroquin, "Half-quadratic cost functions for phase unwrapping," Opt. Lett. 29, 504-506 (2004)
http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-29-5-504


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References

  1. J. L. Marroquin and M. Rivera, J. Opt. Soc. Am. A 12, 2393 (1995).
  2. M. J. Black and A. Rangarajan, Int. J. Comput. Vision 19, 57 (1996).
  3. P. Charbonnier, L. Blanc-Féraud, G. Aubert, and M. Barlaud, IEEE Trans. Image Process. 6, 298 (1997).
  4. M. Rivera and J. L. Marroquin, Image Vision Comput. 21, 345 (2003).
  5. M. Rivera and J. L. Marroquin, Comput. Vision Image Understand. 88, 76 (2002).
  6. D. C. Ghiglia and L. A. Romero, J. Opt. Soc. Am. A 13, 1999 (1996).

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