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A Variational Model for Wrapped Phase Denoising

Author

Listed:
  • Ivan May-Cen

    (CLIR at Facultad de Matematicas, Universidad Autonoma de Yucatan, Merida 97205, Mexico
    Tecnológico Nacional de México Campus Progreso, Progreso 97320, Mexico
    These authors contributed equally to this work.)

  • Ricardo Legarda-Saenz

    (CLIR at Facultad de Matematicas, Universidad Autonoma de Yucatan, Merida 97205, Mexico
    These authors contributed equally to this work.)

  • Carlos Brito-Loeza

    (CLIR at Facultad de Matematicas, Universidad Autonoma de Yucatan, Merida 97205, Mexico
    These authors contributed equally to this work.)

Abstract

This paper presents a variational model for the denoising of wrapped phase images. By enforcing the required Pythagorean trigonometric identity between the real and imaginary components of the signal, this model improves the signal-to-noise ratio of the restored signal. To preserve phase map discontinuities, the model is based on total variation. The existence and uniqueness of the model’s solution are demonstrated using standard techniques. In addition, the convergence of a rapid fixed-point method to determine the numerical solution is demonstrated. Experiments on both synthetic and actual patterns validate the model’s performance.

Suggested Citation

  • Ivan May-Cen & Ricardo Legarda-Saenz & Carlos Brito-Loeza, 2023. "A Variational Model for Wrapped Phase Denoising," Mathematics, MDPI, vol. 11(12), pages 1-15, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:12:p:2618-:d:1166561
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