Abstract

A new, to our knowledge, algorithm for the phase unwrapping (PU) problem that is based on stochastic relaxation is proposed and analyzed. Unlike regularization schemes previously proposed to handle this problem, our approach dispells the following two assumptions about the solution: a Gaussian model for noise and the magnitude of the true phase-field gradient’s being less than π everywhere. We formulate PU as a constrained optimization problem for the field of integer multiples of 2π, which must be added to the wrapped phase gradient to recover the true phase gradient. By solving the optimization problem using simulated annealing with constraints, one can obtain a consistent solution under difficult conditions resulting from noise and undersampling. Results from synthetic test images are reported.

© 1998 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
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1995 (3)

1994 (2)

1992 (1)

N. H. Ching, D. Rosenfeld, M. Braun, “Two-dimensional phase unwrapping using a minimum spanning tree algorithm,” IEEE Trans. Image Process. 1, 355–365 (1992).
[CrossRef] [PubMed]

1989 (1)

1988 (1)

R. M. Goldstein, H. A. Zebker, C. L. Werner, “Satellite radar interferometry: two-dimensional phase unwrapping,” Radio Sci. 23, 713–720 (1988).
[CrossRef]

1987 (1)

1986 (1)

H. A. Zebker, R. M. Goldstein, “Topographic mapping from interferometric synthetic aperture radar observations,” J. Geophys. Res. 91, (B5), 4993–4999 (1986).
[CrossRef]

1985 (2)

S. Nakadate, H. Saito, “Fringe scanning speckle-pattern interferometry,” Appl. Opt. 24, 2172–2180 (1985).
[CrossRef] [PubMed]

H. P. Hjalmarson, L. A. Romero, D. C. Ghiglia, E. D. Jones, C. B. Norris, “Extraction of phonon density-of-states from optical spectra,” Phys. Rev. B 32, 4300–4303 (1985).
[CrossRef]

1984 (1)

S. Geman, D. Geman, “Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images,” IEEE Trans. Patt. Anal. Machine Intell. 6, 721–741 (1984).
[CrossRef]

1980 (1)

R. J. Noll, “Phase estimates from slope-type wave-front sensors,” J. Opt. Soc. Am. A 68, 139–140 (1980).

1977 (2)

Bamler, R.

Bernabeu, E.

Braun, M.

N. H. Ching, D. Rosenfeld, M. Braun, “Two-dimensional phase unwrapping using a minimum spanning tree algorithm,” IEEE Trans. Image Process. 1, 355–365 (1992).
[CrossRef] [PubMed]

Ching, N. H.

N. H. Ching, D. Rosenfeld, M. Braun, “Two-dimensional phase unwrapping using a minimum spanning tree algorithm,” IEEE Trans. Image Process. 1, 355–365 (1992).
[CrossRef] [PubMed]

Fried, D. L.

Geman, D.

S. Geman, D. Geman, “Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images,” IEEE Trans. Patt. Anal. Machine Intell. 6, 721–741 (1984).
[CrossRef]

D. Geman, “Random fields and inverse problems in imaging,” in Ecole D’Ete de Probabilité de Saint-Flour XVII-1988, Vol. 1427 of Springer-Verlag Lecture Notes in Mathematics Series (Springer Verlag, Berlin, 1990), pp. 113–193.

Geman, S.

S. Geman, D. Geman, “Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images,” IEEE Trans. Patt. Anal. Machine Intell. 6, 721–741 (1984).
[CrossRef]

Ghiglia, D. C.

Goldstein, R. M.

R. M. Goldstein, H. A. Zebker, C. L. Werner, “Satellite radar interferometry: two-dimensional phase unwrapping,” Radio Sci. 23, 713–720 (1988).
[CrossRef]

H. A. Zebker, R. M. Goldstein, “Topographic mapping from interferometric synthetic aperture radar observations,” J. Geophys. Res. 91, (B5), 4993–4999 (1986).
[CrossRef]

Gonzáles-Cano, A.

Hjalmarson, H. P.

H. P. Hjalmarson, L. A. Romero, D. C. Ghiglia, E. D. Jones, C. B. Norris, “Extraction of phonon density-of-states from optical spectra,” Phys. Rev. B 32, 4300–4303 (1985).
[CrossRef]

Hudgin, R. H.

Huntley, J. M.

Jones, E. D.

H. P. Hjalmarson, L. A. Romero, D. C. Ghiglia, E. D. Jones, C. B. Norris, “Extraction of phonon density-of-states from optical spectra,” Phys. Rev. B 32, 4300–4303 (1985).
[CrossRef]

Just, D.

Marroquin, J. L.

Mastin, G. A.

Nakadate, S.

Noll, R. J.

R. J. Noll, “Phase estimates from slope-type wave-front sensors,” J. Opt. Soc. Am. A 68, 139–140 (1980).

Norris, C. B.

H. P. Hjalmarson, L. A. Romero, D. C. Ghiglia, E. D. Jones, C. B. Norris, “Extraction of phonon density-of-states from optical spectra,” Phys. Rev. B 32, 4300–4303 (1985).
[CrossRef]

Oppenhein, A. V.

A. V. Oppenhein, R. W. Schafer, Digital Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1975).

Quiroga, J. A.

Rivera, M.

Rodriguez-Vera, R.

Romero, L. A.

Rosenfeld, D.

N. H. Ching, D. Rosenfeld, M. Braun, “Two-dimensional phase unwrapping using a minimum spanning tree algorithm,” IEEE Trans. Image Process. 1, 355–365 (1992).
[CrossRef] [PubMed]

Saito, H.

Schafer, R. W.

A. V. Oppenhein, R. W. Schafer, Digital Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1975).

Servin, M.

Tapia, M.

Werner, C. L.

R. M. Goldstein, H. A. Zebker, C. L. Werner, “Satellite radar interferometry: two-dimensional phase unwrapping,” Radio Sci. 23, 713–720 (1988).
[CrossRef]

Zebker, H. A.

R. M. Goldstein, H. A. Zebker, C. L. Werner, “Satellite radar interferometry: two-dimensional phase unwrapping,” Radio Sci. 23, 713–720 (1988).
[CrossRef]

H. A. Zebker, R. M. Goldstein, “Topographic mapping from interferometric synthetic aperture radar observations,” J. Geophys. Res. 91, (B5), 4993–4999 (1986).
[CrossRef]

Appl. Opt. (4)

IEEE Trans. Image Process. (1)

N. H. Ching, D. Rosenfeld, M. Braun, “Two-dimensional phase unwrapping using a minimum spanning tree algorithm,” IEEE Trans. Image Process. 1, 355–365 (1992).
[CrossRef] [PubMed]

IEEE Trans. Patt. Anal. Machine Intell. (1)

S. Geman, D. Geman, “Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images,” IEEE Trans. Patt. Anal. Machine Intell. 6, 721–741 (1984).
[CrossRef]

J. Geophys. Res. (1)

H. A. Zebker, R. M. Goldstein, “Topographic mapping from interferometric synthetic aperture radar observations,” J. Geophys. Res. 91, (B5), 4993–4999 (1986).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (5)

Phys. Rev. B (1)

H. P. Hjalmarson, L. A. Romero, D. C. Ghiglia, E. D. Jones, C. B. Norris, “Extraction of phonon density-of-states from optical spectra,” Phys. Rev. B 32, 4300–4303 (1985).
[CrossRef]

Radio Sci. (1)

R. M. Goldstein, H. A. Zebker, C. L. Werner, “Satellite radar interferometry: two-dimensional phase unwrapping,” Radio Sci. 23, 713–720 (1988).
[CrossRef]

Other (2)

D. Geman, “Random fields and inverse problems in imaging,” in Ecole D’Ete de Probabilité de Saint-Flour XVII-1988, Vol. 1427 of Springer-Verlag Lecture Notes in Mathematics Series (Springer Verlag, Berlin, 1990), pp. 113–193.

A. V. Oppenhein, R. W. Schafer, Digital Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1975).

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