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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

  • Vol. 12, Iss. 11 — Nov. 1, 1995
  • pp: 2393–2400

Quadratic regularization functionals for phase unwrapping

Jose L. Marroquin and Mariano Rivera  »View Author Affiliations


JOSA A, Vol. 12, Issue 11, pp. 2393-2400 (1995)
http://dx.doi.org/10.1364/JOSAA.12.002393


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Abstract

The problem of unwrapping a noisy principal-value phase field or, equivalently, reconstructing an unwrapped phase field from noisy and possibly incomplete phase differences may be considered ill-posed in the sense of Hadamard. We apply the Thikonov regularization theory to find solutions that correspond to minimizers of positive-definite quadratic cost functionals. These methods may be considered generalizations of the classical least-squares solution to the unwrapping problem; the introduction of the regularization term permits the reduction of noise (even if this noise does not generate integration-path inconsistencies) and the interpolation of the solution over regions with missing data in a stable and controlled way, with a minimum increase of computational complexity. Algorithms for finding direct solutions with transform methods and implementations of iterative procedures are discussed as well. Experimental results on synthetic test images are presented to illustrate the performance of these methods.

© 1995 Optical Society of America

History
Original Manuscript: March 22, 1995
Revised Manuscript: June 19, 1995
Manuscript Accepted: June 20, 1995
Published: November 1, 1995

Citation
Jose L. Marroquin and Mariano Rivera, "Quadratic regularization functionals for phase unwrapping," J. Opt. Soc. Am. A 12, 2393-2400 (1995)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-12-11-2393

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