You are here

Maximum Entropy and MAP Estimation Using Conjugate Gradient Method for Phase Unwrapping

Journal Name:

Publication Year:

Abstract (2. Language): 
We constructed a practical and useful method for phase unwrapping in remote sensing using synthetic aperture radar (SAR) interferometry. First, we constructed a method of maximum entropy to achieve phase unwrapping with high degree of accuracy. Using Monte Carlo simulation for one dimensional artificial wave-front, we found that the method of maximum entropy served an accurate method for phase unwrapping, if we assumed an appropriate model of true prior. Then, in order to construct a practical method, we constructed a deterministic limit of the method of maximum entropy based on a maximum of a posteriori (MAP) estimation using conjugate gradient (CG) method. Using numerical simulation for artificial wave-fronts, we found that the CG method realized phase unwrapping with high degree of accuracy using an appropriate model of true prior. Also, we found that the CG method realized phase unwrapping accurately by utilizing sets of unwrapped phase differences composed from second differences of the observed wave-fronts, even if aliasing occurred at several sampling points.
75-80

REFERENCES

References: 

[1] J. R. Jensen, Remote “Sensing of the Environment: An Earth Resource Perspective (2nd Edition)”, (Prentice Hall; 2 edition) 2006.
[2] D. C. Ghiglia and M. D. Pritt, “Two-Dimensional Phase Unwrapping Theory, Algorithm and Software”, New York: Wiley, 1998, ch. 3.
[3] R. M. Goldstein and H. A. Zebker, “Interferometric radar mapping of ocean currents”, Nature, vol. 328, 1987, pp. 707-709.
[4] D. L. Fried, “Least-square fitting of a wave-front distortion estimate to an array of phase differences measurements”, J. Opt. Soc. Am., vol. 67, 1977, pp. 370-375.
[5] R. H. Hudgin, “Wave-front reconstruction for compensated imaging”, J. Opt. Soc. Am., vol. 67, 1977, pp. 375-378.
[6] H. Takajyo and T. Takahashi, “Least squares phase estimation from phase difference”, J. Opt. Soc. Am. A, vol. 5, 1988, pp. 416-425.
[7] D. C. Ghiglia and L. A. Romero, “Robust two-dimensional weighted and unweighted phase unwrapping that uses fast transforms and iterative method”, J. Opt. Soc. Am. A, vol. 11, 1994, pp. 107-117.
[8] L. Guerriero, G. Nico, G. Pasquariello and Stramaglia, “A new regularization scheme for phase unwrapping”, Appl. Opt. vol. 37, 1998, pp. 3058-3058.
[9] G. Nico, G. Palubinskas and M. Datcu, “Bayesian Approaches to Phase Unwrapping: Theoretical Study”, IEEE Trans. Signal Processing, vol. 48(4), 2000, pp. 2545-2556.
[10] Y. Saika and H. Nishimori, “Statistical-mechanical approach for the problem of phase retrieval using the Q-Ising model”, Progress Theoretical Physics Supplement, vol. 157, 2005, pp. 292-295.
[11] Y. Saika and H. Nishimori, “Statistical-mechanical approaches to the problem of phase retrieval in adaptive optics in astronomy”, J. Phys. : Conf. Ser., vol. 31, 2006, pp. 169-170.
[12] Y. Saika and T. Uezu, “Statistical Mechanics of Phase Unwrapping using the Q-Ising Model”, IEICE Technical Report, NLP2012-12(2012-4), 2012, pp. 61-65.
[13] J. L. Marroquin and M. Rivera, “Quadratic regularization functionals for phase unwrapping”, J. Opt. Soc. Am. A, vol. 12, 1995, pp. 2393-2400.
[14] H. Sakaematsu and Y. Saika, “Statistical Performance of Conjugate Gradient Method for Phase Unwrapping in Adaptive Optics” in Proc. of 2012 12th International Conference on Control, Automation and Systems, Korea, 2012, pp. 1279-1284.

Thank you for copying data from http://www.arastirmax.com