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Half-quadratic cost functions for phase unwrapping.

Mariano Rivera1, Jose L Marroquin

  • 1Centro de Investigacion en Matematicas A.C., Apartado Postal 402, 36000 Guanajuato, Guanajuato, Mexico. mrivera@fractal.cimat.mx

Optics Letters
|March 10, 2004
PubMed
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We developed a robust method for unwrapping noisy phase maps. A nonconvex formulation offers superior performance for phase maps with real discontinuities, improving phase unwrapping accuracy.

Area of Science:

  • Image processing
  • Computational mathematics
  • Signal processing

Background:

  • Phase maps are essential in various imaging techniques.
  • Noisy and discontinuous phase maps present significant unwrapping challenges.
  • Existing methods struggle with real-world phase discontinuities.

Purpose of the Study:

  • To present a generic regularized formulation for phase map unwrapping.
  • To address limitations of convex formulations in the presence of discontinuities.
  • To introduce a nonconvex approach for improved phase unwrapping performance.

Main Methods:

  • Developed a robust half-quadratic regularization framework.
  • Investigated both convex and nonconvex formulations for phase unwrapping.

Related Experiment Videos

  • Employed a parameter continuation strategy for the nonconvex case.

    • Main Results:

    • The convex formulation provides a unique and noise-robust solution.
    • Convex solutions degrade with real phase map discontinuities.
    • The nonconvex formulation demonstrates superior performance on discontinuous phase maps.

    Conclusions:

    • Robust half-quadratic regularization is effective for phase unwrapping.
    • The nonconvex formulation is crucial for handling real phase discontinuities.
    • This work advances phase unwrapping techniques for noisy and complex data.