Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
skip to main content
10.1145/3387168.3387246acmotherconferencesArticle/Chapter ViewAbstractPublication PagesicvispConference Proceedingsconference-collections
research-article

Two-dimensional Phase Unwrapping with Priori Boundary Condition

Published: 25 May 2020 Publication History

Abstract

Phase unwrapping is essential for many applications such as Interferometric synthetic aperture radar, MRI, and X-ray phase imaging etc. In these applications, the phase is determined only in the principal value range of [-π,π). The unwrapping that recover true phase method becomes difficult when the measured object possesses big discontinuity. In these minimum norm methods, for unwrapping, it is needed to minimize the difference between the gradient of the wrapped phase and that of the unwrapped phase using the Lp norm. Many authors suggest that the goal of phase unwrapping should be minimizing the Lo norm problem. However, previous methods have reached its limits as this is a nonconvex problem. To solve this difficulty, in this paper we used boundary information as the priori condition which is suitable in many applications. Then the unwrapped phase is given by solving a Lp (p ≥ 1) norm minimization problem that belongs to convex optimization. The simulation results demonstrate that our method is effective.

References

[1]
A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, "Demonstration of X-Ray Talbot interferometry," Jpn. J. Appl. Phys. 42, L866--L868, 2003.
[2]
C. Chen, H. Zebker, "Network approaches to two-dimensional phase unwrapping: Intractability and two new algorithms", J. Opt. Soc. Amer., A, vol. 17, no. 3, pp. 401--414, 2000.
[3]
D. Ghiglia, and M. Pritt, "Two-Dimensional Phase Unwrapping. Theory, Algorithms, and Software", New York: Wiley, 1998.
[4]
D. Ghiglia, L. A. Romero, "Minimum Lp-norm two-dimensional phase unwrapping", J. Opt. Soc. Amer., A, vol. 13, no. 10, pp. 1999--2013, 1996.
[5]
D. Martin, C. Fowlkes, D. Tal, and J. Malik, 2001. A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics. In Proc. 8th Int. Conf. Comput. Vis. 2, 416--423, 2001.
[6]
D. Massonnet, K. L. Feigl, "Radar interferometry and its application to changes in the earth's surface", Rev. Geophys., vol. 36, no. 4, pp. 441--500, 1998.
[7]
F. Pfeiffer, T. Weitkamp, B. Oliver, D. Christian, "Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources", Nature Phys. Vol 2, pp. 258--261, 2006.
[8]
J. Bioucas-Dias, and G. Valadão, "Phase unwrapping via graph cuts", IEEE Trans. Image Process., vol. 16, no. 3, pp.698 -709, 2007.
[9]
K. Itoh, "Analysis of the phase unwrapping problem", Appl. Opt. vol. 21, no. 14, pp. 2470--2470, 1982.
[10]
M. Costantini, "A novel phase unwrapping method based on network programing," IEEE Trans. Geosci. Remote Sens., vol. 36, no. 3, pp. 813--821, May, 1998.
[11]
P. A. Rosen, S. Hensley, I. R. Joughin, F. K. Li, S. N. Madsen E. Rodriguez, and R. Goldstein, "Synthetic aperture radar interferometry", Proc. IEEE, vol. 88, no. 3, pp. 333--382, 2000.
[12]
P. Jezzard, and R. S. Balaban, "Correction for geometric distortion in echo planar images from B_0 field variations", Magnetic Resonance in medicine, vol. 34, pp. 65--73, 1995.
[13]
R. Goldstein, H. Zebker, and C. Werner, "Satellite radar interferometry: Two-dimensional phase unwrapping, " in Proc. Symp. Ionospheric Effects on Communication and Related Systems, vol. 23, pp. 713--720, 1998.
[14]
S. Madsen, H. Zebker, and J. Martin, "Topographic mapping using radar interferometry: Processing techniques," IEEE Trans. Geosci. Remote Sens., vol. 31, no. 1, pp. 246--256, 1993.
[15]
T. Flynn, "Two-dimensional phase unwrapping with minimum weighted discontinuity", J. Opt. Soc. Amer. A, vol. 14, no. 10, pp. 2692--2701, 1997.
[16]
T. Weitkamp, A. Diaz, C. David, D. Christian, F. Pfeiffer, M. Stampanoni, P. Cloetens, E. Ziegler, "Quantitative X-ray phase imaging with a grating interferometer", Opt. Express vol. 13, pp. 6296--6304, 2005.
[17]
U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, D. Psaltis, and M. Unser, "Isotropic inverse-problem approach for two-dimensional phase unwrapping," J. Opt. Soc. Am. A 32, 1092--1100, 2015.
[18]
V. Kolmogorov, R. Zabih, "What Energy Functions Can Be Minimized via Graph Cuts?", IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 26, no. 2, pp. 147--159, 2004.
[19]
W. Xu and I. Cumming, "A region growing algorithm for insar phase unwrapping," in Proc. Int. Geoscience and Remote Sensing Symp., Lincoln, NE, vol. 4, pp. 2044--2046, 1996

Index Terms

  1. Two-dimensional Phase Unwrapping with Priori Boundary Condition

    Recommendations

    Comments

    Information & Contributors

    Information

    Published In

    cover image ACM Other conferences
    ICVISP 2019: Proceedings of the 3rd International Conference on Vision, Image and Signal Processing
    August 2019
    584 pages
    ISBN:9781450376259
    DOI:10.1145/3387168
    Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

    Publisher

    Association for Computing Machinery

    New York, NY, United States

    Publication History

    Published: 25 May 2020

    Permissions

    Request permissions for this article.

    Check for updates

    Author Tags

    1. Minimum norm
    2. Nonconvex
    3. Phase unwrapping
    4. Priori condition

    Qualifiers

    • Research-article
    • Research
    • Refereed limited

    Funding Sources

    • JST-ERATO
    • JSPS KAKENHI

    Conference

    ICVISP 2019

    Acceptance Rates

    ICVISP 2019 Paper Acceptance Rate 126 of 277 submissions, 45%;
    Overall Acceptance Rate 186 of 424 submissions, 44%

    Contributors

    Other Metrics

    Bibliometrics & Citations

    Bibliometrics

    Article Metrics

    • 0
      Total Citations
    • 53
      Total Downloads
    • Downloads (Last 12 months)2
    • Downloads (Last 6 weeks)0
    Reflects downloads up to 25 Feb 2025

    Other Metrics

    Citations

    View Options

    Login options

    View options

    PDF

    View or Download as a PDF file.

    PDF

    eReader

    View online with eReader.

    eReader

    Figures

    Tables

    Media

    Share

    Share

    Share this Publication link

    Share on social media