CAPE: Combinatorial absolute phase estimation

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

Volumn 26, Issue 9, 2009, Pages 2093-2106

  Valadão, Gonçalo ^a   Bioucas Dias, José ^a  

^a INSTITUTO DE TELECOMUNICAÇÕES   (Portugal)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTER SCIENCE; HIDDEN MARKOV MODELS;

ABSOLUTE PHASE; BAYESIAN; BINARY OPTIMIZATION; DE-NOISING; FIRST-ORDER; MARKOV RANDOM FIELDS; MAXIMUM A POSTERIORI PROBABILITIES; NON-LINEARITY; PHASE UNWRAPPING; PIECEWISE SMOOTH; SUB-OPTIMAL ALGORITHMS;

COMBINATORIAL MATHEMATICS;

EID: 70249111830     PISSN: 10847529     EISSN: 15208532     Source Type: Journal    
DOI: 10.1364/JOSAA.26.002093     Document Type: Article

References (51)

1. P. Rosen, S. Hensley, I. Joughin, F. LI, S. Madsen, E. Rodriguez, and R. Goldstein, "Synthetic aperture radar interferometry," Proc. IEEE 88, 333-382 (2000).
2. P. Lauterbur, "Image formation by induced local interactions: examples employing nuclear magnetic resonance," Nature 242, 190-191 (1973).
3. D. L. Fried, "Adaptive optics wave function reconstruction and phase unwrapping when branch points are present," Opt. Commun. 200, 43-72 (2001).
4. T. Venema and J. Schmidt, "Optical phase unwrapping in the presence of branch points," Opt. Express 16, 6985-6998 (2008).
5. S. Pandit, N. Jordache, and G. Joshi, "Data-dependent systems methodology for noise-insensitive phase unwrapping in laser interferometric surface characterization," J. Opt. Soc. Am. A 11, 2584-2592 (1994).
6. A. Devaney, "Diffraction tomographic reconstruction from intensity data," IEEE Trans. Image Process. 1, 221-228 (1992).
7. A. Rauscher, M. Barth, J. Reichenbach, R. Stollberger, and E. Moser, "Automated unwrapping of MR phase images applied to BOLD MR-venography at 3 Tesla," J. Magn. Reson. Imaging 18, 175-180 (2003).
8. A. Manduca, T. Oliphant, M. Dresner, J. Mahowald, S. Kruse, E. Amromin, J. Felmlee, J. Greenleaf, and R. Ehman, "Magnetic resonance elastography: non-invasive mapping of tissue elasticity," Med. Image Anal. 5, 237-254 (2001).
9. M. C. Roggemann and B. M. Welsh, Imaging Through Turbulence (CRC, 1996).
10. K. Itoh, "Analysis of the phase unwrapping problem," Appl. Opt. 21, 2470 (1982).
11. J. Hadamard, "Sur les problèmes aux dérivées partielles et leur signification physique," Princeton University Bulletin (1902), pp. 49-52.
12. D. Ghiglia and M. Pritt, Two-Dimensional Phase Unwrapping. Theory, Algorithms, and Software (Wiley, 1998).
13. J. Dias and J. Leitão, "The ZnM algorithm for interferometric image reconstruction in SAR/SAS," IEEE Trans. Image Process. 11, 408-422 (2002).
14. V. Katkovnik, J. Astola, and K. Egiazarian, "Phase local approximation (phasela) technique for phase unwrap from noisy data," IEEE Trans. Image Process. 17, 833-846 (2008).
15. R. Goldstein, H. Zebker, and C. Werner, "Satellite radar interferometry: two-dimensional phase unwrapping," in Symposium on the Ionospheric Effects on Communication and Related Systems (Radio Science, 1988), Vol.23, pp. 713-720.
16. J. Huntley, "Noise-immune phase unwrapping algorithm," Appl. Opt. 28, 3268-3270 (1989).
17. T. Flynn, "Two-dimensional phase unwrapping with minimum weighted discontinuity," J. Opt. Soc. Am. A 14, 2692-2701 (1997).
18. D. Ghiglia and L. Romero, "Minimum Lp-norm two- dimensional phase unwrapping," J. Opt. Soc. Am. A 14, 1-15 (1996).
19. M. Costantini, "A novel phase unwrapping method based on network programing," IEEE Trans. Geosci. Remote Sens. 36, 813-821 (1998).
20. J. Marroquin and M. Rivera, "Quadratic regularization functionals for phase unwrapping," J. Opt. Soc. Am. A 12, 2393-2400 (1995).
21. J. Leitão and M. Figueiredo, "Absolute phase image reconstruction: a stochastic nonlinear filtering approach," IEEE Trans. Image Process. 7, 868-882 (1997).
22. M. Datcu and G. Palubinskas, "Multiscale Bayesian height estimation from insar using a fractal prior," Proc. SPIE 3497, 155-163 (1998).
23. G. Nico, G. Palubinskas, and M. Datcu, "Bayesian approach to phase unwrapping: theoretical study," IEEE Trans. Signal Process. 48, 2545-2556 (2000).
24. M. Rivera and J. Marroquin, "Half-quadratic cost functions for phase unwrapping," Opt. Lett. 29, 504-506 (2004).
25. J. Bioucas-Dias and G. Valadão, "Phase unwrapping via graph cuts," IEEE Trans. Image Process. 16, 698-709 (2007).
26. J. Bioucas-Dias, V. Katkovnik, J. Astola, and K. Egiazarian, "Absolute phase estimation: adaptive local denoising and global unwrapping," Appl. Opt. 47, 5358-5369 (2008).
27. R. Ahuja, D. Hochbaum, and J. Orlin, "Solving the convex cost integer dual network flow problem," Manage. Sci. 49, 950-964 (2003).
28. M. Iri, Network Flow, Transportation and Scheduling- Theory and Algorithms (Academic, 1969).
29. K. Murota, "On steepest descent algorithms for discrete convex functions," SIAM J. Optim. 14, 699-707 (2003).
30. R. Rockafellar, Network Flows and Monotropic Optimization (Wiley, 1984).
31. J. Bioucas-Dias and G. Valadao, "Discontinuity preserving phase unwrapping using graph cuts," in Energy Minimization Methods in Computer Vision and Pattern Recognition, A. Rangarajan, B. Vemuri, and A. Yuille, eds., Vol.3757 of Lecture Notes in Computer Science (Springer, 2005), pp. 268-284.
32. Y. Boykov and V. Kolmogorov, "An experimental comparison of min-cut/max-flow algorithms for energy minimization in vision," IEEE Trans. Pattern Anal. Mach. Intell. 26, 1124-1137 (2004).
33. V. Kolmogorov, "Primal-dual algorithm for convex Markov random fields," Tech. Rep. MSR-TR-2005-2117 (Microsoft Research, 2005).
34. V. Kolmogorov and A. Shioura, "New algorithms for the dual of the convex cost network flow problem with application to computer vision." Tech. Rep. (University College London, 2007).
35. J. Darbon, "Composants logiciels et algorithmes de minimisation exacte d'energies dedies au traitement des images," Ph.D. thesis (Ecole Nationale Superieure des Telecommunications, 2005).
36. K. Murota, Discrete Convex Analysis (Society for Industrial and Applied Mathematics, 2003).
37. H. Ishikawa, "Exact optimization for Markov random fields with convex priors," IEEE Trans. Pattern Anal. Mach. Intell. 25, 1333-1336 (2003).
38. J. Darbon, "Global optimization for first order Markov random fields with submodular priors," Discrete Appl. Math. (to be published).
39. V. Kolmogorov and R. Zabih, "What energy functions can be minimized via graph cuts?" IEEE Trans. Pattern Anal. Mach. Intell. 26, 147-159 (2004).
40. K. Lange, Optimization (Springer Verlag, 2004).
41. Y. Boykov, O. Veksler, and R. Zabih, "Fast approximate energy minimization via graph cuts," IEEE Trans. Pattern Anal. Mach. Intell. 23, 1222-1239 (2001).
42. C. Chen, "Statistical-cost network-flow approaches to two- dimensional phase unwrapping for radar interferometry," Ph.D. thesis (Stanford University, 2001).
43. A. Blake and A. Zisserman, Visual Reconstruction (MIT Press, 1987).
44. D. Geman and G. Reynolds, "Constrained restoration and the recovery of discontinuities," IEEE Trans. Pattern Anal. Mach. Intell. 14, 367-383 (1992).
45. S.Z. Li, Markov Random Field Modeling in Computer Vision, Vol.9 of Computer Science Workbench (Springer- Verlag, 1995).
46. D. Greig, B. Porteous, and A. Seheult, "Exact maximum a posteriory estimation for binary images," J. R. Stat. Soc. Ser. B (Methodol.) 51, 271-279 (1989).
47. R. Szeliski, R. Zabih, D. Scharstein, O. Veksler, V. Kolmogorov, A. Agarwala, M. Tappen, and C. Rother, "A comparative study of energy minimization methods for Markov random fields with smoothness-based priors," IEEE Trans. Pattern Anal. Mach. Intell. 30, 1068-1080 (2008).
48. L. Ford and D. Fulkerson, Flows in Networks (Princeton Univ. Press, 1962).
49. C. Rother, V. Kolmogorov, V. Lempitsky, and M. Szummer, "Optimizing binary MRFs via extended roof duality," in IEEE Conference on Computer Vision and Pattern Recognition 2007. CVPR, '07 (IEEE, 2007), pp. 1-8.
50. P. Kohli and P. Torr, "Dynamic graph cuts for efficient inference in Markov random fields," IEEE Trans. Pattern Anal. Mach. Intell. 29, 2079-2088 (2007).
51. Y. Boykov and V. Kolmogorov, "Computing geodesics and minimal surfaces via graph cuts," in Proceedings of Ninth IEEE International Conference on Computer Vision 2003 (IEEE, 2003), Vol.1, pp. 26-33.