Minimum Lp-norm two-dimensional phase unwrapping

Journal of the Optical Society of America A: Optics and Image Science, and Vision

Volumn 13, Issue 10, 1996, Pages 1999-2013

  Ghiglia, Dennis C ^a   Romero, Louis A ^a  

^a SANDIA NATIONAL LABORATORIES   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0008632780     PISSN: 10847529     EISSN: 15208532     Source Type: Journal    
DOI: 10.1364/JOSAA.13.001999     Document Type: Article

References (41)

1. L. C. Graham, “Synthetic interferometer radar for topographic mapping,” Proc. IEEE 62, 763–768 (1974).
2. R. M. Goldstein, H. A. Zebker, and C. L. Werner, “Satellite radar interferometry: two-dimensional phase unwrapping,” Radio Sci. 23, 713–720 (1988).
3. H. A. Zebker and R. M. Goldstein, “Topographic mapping from interferometric synthetic aperture radar observations,” J. Geophys. Res. 91, 4993–4999 (1986).
4. F. K. Li and R. M. Goldstein, “Studies of multibaseline spa-ceborne interferometric synthetic aperture radars,” IEEE Trans. Geosci. Remote Sens. 28, 88–97 (1990).
5. A. L. Gray and P. J. Farris-Manning, “Repeat-pass interferometry with airborne synthetic aperture radar,” IEEE Trans. Geosci. Remote Sens. 31, 180–191 (1993).
6. P. H. Eichel, D. C. Ghiglia, C. V. Jakowatz Jr., P. A. Thompson, and D. E. Wahl, “Spotlight SAR interferometry for terrain elevation mapping and interferometric change detection,” Rep. SAND93-2072J (Sandia National Laboratories, Albuquerque, N.M., 1993).
7. D. Massonnet, M. Rossi, C. Carmona, F. Adragna, G. Pelt-zer, K. Feigl, and T. Rabaute, “The displacement field of the Landers earthquake mapped by radar interferometry,” Nature (London) 364, 138–142 (1993).
8. K. J. Gåsvik, Optical Metrology, 2nd ed. (Wiley, Chichester, UK, 1995).
9. D. W. Robinson and G. T. Reid, Interferogram Analysis: Digital Fringe Pattern Measurement Techniques (Institute of Physics, Bristol, UK, 1993).
10. D. L. Fried, “Least-squares fitting a wave-front distortion estimate to an array of phase-difference measurements,” J. Opt. Soc. Am. 67, 370–375 (1977).
11. R. H. Hudgin, “Wave-front reconstruction for compensated imaging,” J. Opt. Soc. Am. 67, 375–378 (1977).
12. R. J. Noll, “Phase estimates from slope-type wave-front sensors,” J. Opt. Soc. Am. 68, 139–140 (1978).
13. 0 inhomogeneity correction,” Magn. Reson. Med. 18, 371–383 (1991).
14. J. Szumowski, W. R. Coshow, F. Li, and S. F. Quinn, “Phase unwrapping in the three-point Dixon method for fat suppression MR imaging,” Radiology, 192, 555–561 (1994).
15. S. M. Song, S. Napel, N. J. Pelc, and G. H. Glover, “Phase unwrapping of MR phase images using Poisson equation,” IEEE Trans. Image Process. 4, 667–676 (1995).
16. K. Itoh, “Analysis of the phase unwrapping problem,” Appl. Opt. 21, 2470 (1982).
17. D. C. Ghiglia, G. A. Mastin, and L. A. Romero, “Cellular automata method for phase unwrapping,” J. Opt. Soc. Am. A 4, 267–280 (1987).
18. J. M. Huntley, “Noise-immune phase unwrapping algorithm,” Appl. Opt. 28, 3268–3270 (1989).
19. D. J. Bone, “Fourier fringe analysis: the two-dimensional phase unwrapping problem,” Appl. Opt. 30, 3627–3632
20. R. Cusack, J. M. Huntley, and H. T. Goldrein, “Improved noise-immune phase-unwrapping algorithm,” Appl. Opt. 34, 781–789 (1995).
21. J. A. Quiroga, A. Gonziilez-Cano, and E. Bernabeu, “Stable-marriages algorithm for preprocessing phase maps with discontinuity sources,” Appl. Opt. 34, 5029–5038 (1995).
22. J. R. Buckland, J. M. Huntley, and S. R. E. Turner, “Unwrapping noisy phase maps by use of a minimum-cost-matching algorithm,” Appl. Opt. 34, 5100–5108 (1995).
23. N. H. Ching, D. Rosenfeld, and M. Braun, “Twodimensional phase unwrapping using a minimum spanning tree algorithm,” IEEE Trans. Image Process. 1, 355–365
24. B. R. Hunt, “Matrix formulation of the reconstruction of phase values from phase differences,” J. Opt. Soc. Am. 69, 393–399 (1979).
25. H. Takajo and T. Takahashi, “Least-squares phase estimation from phase differences,” J. Opt. Soc. Am. A 5, 416–425 (1988).
26. H. Takajo and T. Takahashi, “Noniterative method for obtaining the exact solution for the normal equation in least-squares phase estimation from the phase difference,” J. Opt. Soc. Am. A 5, 1818–1827 (1988).
27. D. C. Ghiglia and L. A. Romero, “Direct phase estimation from phase differences using fast elliptic partial differential equation solvers,” Opt. Lett. 14, 1107–1109 (1989).
28. B. L. Busbee, G. H. Gollub, and C. W. Nielson, “On direct methods for solving Poisson’s equations,” SIAM J. Numer. Anal. 7, 627–656 (1970).
29. D. C. Ghiglia and L. A. Romero, “Robust two-dimensional weighted and unweighted phase unwrapping that uses fast transforms and iterative methods,” J. Opt. Soc. Am. A 11, 107–117 (1994).
30. J. L. Marroquin and M. Rivera, “Quadratic regularization functionals for phase unwrapping,” J. Opt. Soc. Am. A 12, 2393–2400 (1995).
31. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vet-terling, Numerical Recipes: The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, Cambridge, 1992), Chap. 18.
32. D. Just, Deutsche Forschungsanstalt für Luft-und Raum-fahrt (DLR), Wessling, Germany, July 1995 (personal communication).
33. D. Just, N. Adam, M. Schwäbisch, and R. Bamler, “Comparison of phase unwrapping algorithms for SAR interfero-grams,” presented at the International Geoscience and Remote Sensing Symposium (IGARSS’95), Firenze, Italy, July 10–14, 1995.
34. M. D. Pritt, Loral Federal Systems, Gaithersburg, Md., September 1995 (personal communication).
35. G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists, 4th ed. (Academic, San Diego, 1995), Chap. 17.
36. G. M. Ewing, Calculus of Variations with Applications (Dover, New York, 1985).
37. M. D. Pritt, “Phase unwrapping by means of multigrid techniques for inteferometric SAR,” IEEE Trans. Geosci. Remote Sens. 34, 728–738 (1996).
38. M. D. Pritt, “Multigrid phase unwrapping for interferometric SAR,” in Proceedings of the IEEE International Geoscience Remote Sensing Symposium (IEEE, Au:city, 1995), Vol. 1, pp. 562–564.
39. J. M. Huntley and J. R. Buckland, “Characterization of sources of 2w phase discontinuity in speckle interfero-grams,” J. Opt. Soc. Am. A 12, 1990–1996 (1995).
40. J. S. Lim, “The discretäüüe cosine transform,” in TwoDimensional Signal and Image Processing (Prentice-Hall, Englewood Cliffs, N.J., 1990), pp. 148–157.
41. M. D. Pritt and J. S. Shipman, “Least-squares twodimensional phase unwrapping using FFTs,” IEEE Trans. Geosci. Remote Sens. 32, 706–708 (1994).