Abstract
Phase of backscattered signals is used in various systems such as digital elevation model and detecting topographic change. Phase of received signal is circular and varies only between 0 and 2π radians. Thus, an ambiguity emerges when phase exceeds 2π radians. In such cases, ambiguity needs to be corrected in a process known as phase unwrapping. The present study uses algorithms including Goldstein, quality-guided, mask cut and least squares for phase unwrapping and a systematic, combined and extended method is presented. We investigate the required conditions to have paired residues since these residues are highly useful for proper placement of branch cut. The main challenge for this study is the proper placement of branch cut which is used to prevent path dependence in phase unwrapping. To achieve this, the present work makes use of combined and extended method to investigate the principles of branch cuts.
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Osmanoglu, B., Dixon, T.H., Wdowinski, S., Cabral-Cano, E.: On the importance of path for phase unwrapping in synthetic aperture radar interferometry. Appl. Opt. 50(19), 3205–3220 (2011)
Zhong, H., Tang, J., Zhang, S., Zhang, X.: A quality-guided and local minimum discontinuity based phase unwrapping algorithm for InSAR/InSAS interferograms. IEEE Geosci. Remote Sens. Lett. 11(1), 215–219 (2014)
Chavez, S., Xiang, Q., An, L.: Understanding phase maps in MRI: a new cutline phase unwrapping method. IEEE Trans. Med. Imaging 21(8), 966–977 (2002)
Richards, M.A.: A beginner’s guide to interferometric SAR concepts and signal processing. IEEE Aerosp. Electron. Syst. 22(9), 5–29 (2007)
Richards, J.A.: Remote sensing with imaging radar. Springer, Berlin (2009)
Ghiglia, D.C., Pritt, M.D.: Two-Dimensional Phase Unwrapping: Theory, Algorithms and Software. Wiley, New York (1998)
Yoon, S.K., Kim, S.: Modified Goldstein algorithm using boundary information in phase unwrapping. In: Digital Holography and Three-Dimensional Imaging 2009. Vancouver (2009)
Bone, D.J.: Fourier fringe analysis: the two-dimensional phase unwrapping problem. Appl. Opt. 30(25), 3627–3632 (1991)
Zhao, M., Huang, L., Zhang, Q.C., Su, X.Y., Asundi, A., Kemao, Q.: Quality-guided phase unwrapping technique: comparison of quality maps and guiding strategies. Appl. Opt. 50(33), 6214–6224 (2011)
Arevalillo-Herráez, M., Villatoro, F.R., Gdeisat, M.A.: A robust and simple measure for quality-guided 2D phase unwrapping algorithms. IEEE Trans. Image Process. 25(6), 2601–2609 (2016)
Prati, C., Giani, M., Leuratti, N.: SAR interferometry: a 2-D phase unwrapping technique based on phase and absolute values information. In: 10th Annual International Symposium Geoscience and Remote Sensing, pp. 2043–2046. Maryland (1990)
Flynn, T.J.: Two-dimensional phase unwrapping with minimum weighted discontinuity. Opt. Soc. Am. A 14(10), 2692–2701 (1997)
Ghiglia, D.C., Romero, L.A.: Minimum Lp-norm two-dimensional phase unwrapping. Opt. Soc. Am. A 13(10), 1–15 (1996)
Zhang, X., Zheng, Y., Wang, Z. A new method of nonlinear least squares phase unwrapping. In: Proceedings of 2013 2nd International Conference on Measurement, Information and Control. Harbin, pp. 720–723. China (2013)
Sao, A.K., Yegnanarayana, B.: On the use of phase of the Fourier transform for face recognition under variations in illumination. SIViP 4(3), 353–358 (2009)
Pandey, N., Singh, M.P., Ghosh, A., Khare, K.: Optical surface measurement using accurate carrier estimation in Fourier transform fringe analysis and phase unwrapping based upon transport of intensity equation. Optics 47(3), 389–395 (2018)
Costantini, M.: Novel phase unwrapping method based on network programming. IEEE Trans. Geosci. Remote Sens. 36(3), 813–821 (1998)
Syakrani, N., Mengko, T.L., Suksmono, A.B., Baskoro, E.T.: Comparison of PUMA and CUNWRAP to 2-D phase unwrapping. In: Proceedings of the 2011 International Conference on Electrical Engineering and Informatics. Bandung. Indonesia (2011)
Bioucas-Dias, J., Valadão, G.: Phase unwrapping via graph cuts. IEEE Trans. Geosci. Remote Sens. 16(3), 698–709 (2007)
Phuc, P.H., Rhee, H., Ghim, Y.: Denoising phase unwrapping algorithm for precise phase shifting interferometry. Korean Phys. Soc. 71(2), 82–87 (2017)
Popov, S.E.: Improved phase unwrapping algorithm based on NVIDIA CUDA. Program. Comput. Softw. 43(1), 24–36 (2017)
Pinel-Puysségur, B., Lasserre, C., Benoit, A., Jolivet, R., Doin, M., Champenois, J.: A simple phase unwrapping errors correction algorithm based on phase closure analysis. In: International Geoscience and Remote Sensing Symposium, pp. 2212–2215 (2018)
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Research is supported by School of Electrical and Computer Engineering, Shiraz University.
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Marhamati, R., Masnadi-Shirazi, M.A. The principles of proper placement of branch cut in phase unwrapping using combined and extended methods based on residue searching. SIViP 14, 593–600 (2020). https://doi.org/10.1007/s11760-019-01588-0
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DOI: https://doi.org/10.1007/s11760-019-01588-0