Abstract

In the past we proposed a multidimensional speckle noise model to which we now include systematic phase variation effects. This extension makes it possible to define what is believed to be a novel coherence model able to identify the different sources of bias when coherence is estimated on multidimensional synthetic radar aperture (SAR) data. On the one hand, low coherence biases are basically due to the complex additive speckle noise component of the Hermitian product of two SAR images. On the other hand, the availability of the coherence model permits us to quantify the bias due to topography when multilook filtering is considered, permitting us to establish the conditions upon which information may be estimated independently of topography. Based on the coherence model, two coherence estimation approaches, aiming to reduce the different biases, are proposed. Results with simulated and experimental polarimetric and interferometric SAR data illustrate and validate both, the coherence model and the coherence estimation algorithms.

© 2007 Optical Society of America

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  1. R. Bamler and P. Hartl, "Synthetic aperture radar interferometry," Inverse Probl. 14, R1-R54 (1998).
    [CrossRef]
  2. J. P. Matthews, H. Kamada, S. Okuyama, Y. Yusa, and H. Shimizu, "Surface height adjustments in pyroclastic flow deposits observed at Unzen volcano by JERS-1 SAR interferometry," J. Volcanol. Geotherm. Res. 125, 247-270 (2003).
    [CrossRef]
  3. M. E. Engdahl, J. T. Pulliainen, and M. T. Hallikainen, "Boreal forest coherence-based measures on interferometric pair suitability for operational stem volume retrieval," IEEE Geosci. Remote Sensing Lett. 1, 228-231 (2004).
    [CrossRef]
  4. J. Hyyppä, H. Hyyppä, M. Inkinena, M. Engdahla, S. Linkob, and Y. H. Zhuc, "Accuracy comparison of various remote sensing data sources in the retrieval of forest stand attributes," Forest Ecol. Manage. 128, 109-120 (2000).
    [CrossRef]
  5. E. W. Hoen and H. A. Zebker, "Topography-driven variations in backscatter strength and depth observed over the Greenland Ice Sheet with InSAR," Proceedings of the International Geoscience and Remote Sensing Symposium IGARSS (2000), Vol. 2, pp. 470-472.
  6. T. Strozzi, U. Wegmuller, and C. Matzler, "Using repeat-pass SAR interferometry for mapping wet snow covers," Proceedings of the International Geoscience and Remote Sensing Symposium IGARSS (1998), Vol. 3, pp. 1650-1652.
  7. S. Li, C. Benson, L. Shapiro, and K. Dean, "Aufeis in the Ivishak from Satellite Radar River, Alaska, Interferometry Mapped," Remote Sens. Environ 20, 131-139 (1997).
  8. J. Weydahl, "Analysis of ERS tandem SAR coherence from glaciers, valleys, and fjords ice on Svalbard," IEEE Trans. Geosci. Remote Sensing 39, 2029-2039 (2001).
    [CrossRef]
  9. F. Mattia, T. Le Toan, J. S. Lee, and D. L. Schuler, "On the sensitivity of polarimetric coherence to small and large scale surface roughness," Proceedings of the International Geoscience and Remote Sensing Symposium IGARSS (2003), Vol. 2, pp. 690-692.
  10. D. Kasilingam, D. L. Schuler, J. S. Lee, and S. Malhotra, "Modulation of polarimetric coherence by ocean features," Proceedings of the International Geoscience and Remote Sensing Symposium IGARSS (2002), Vol. 1, pp. 432-434.
  11. H. Wakabayashi, T. Matsuoka, K. Nakamura, and F. Nishio, "Polarimetric Characteristics of sea ice in the sea of Okhotsk observed by airborne L-band SAR," IEEE Trans. Geosci. Remote Sensing 42, 2412-2425 (2004).
    [CrossRef]
  12. D. H. Hoekman and M. J. Quiñones, "Biophysical forest type characterization in the Colombian Amazon by airborne polarimetric SAR," IEEE Trans. Geosci. Remote Sensing 40, 1288-1300 (2002).
    [CrossRef]
  13. S. R. Cloude and K. P. Papathanassiou, "Polarimetric SAR Interferometry," IEEE Trans. Geosci. Remote Sensing 36, 1551-1565 (1998).
    [CrossRef]
  14. J. D. Ballester-Berman, J. M. Lopez-Sanchez, J. Fortuny-Guasch, "Retrieval of biophysical parameters of agricultural crops using polarimetric SAR interferometry," IEEE Trans. Geosci. Remote Sensing 43, 683-694 (2005).
    [CrossRef]
  15. A. Reigber and J. Moreira, "Phase unwrapping by fusion of local and global methods," Proceedings of the International Geoscience and Remote Sensing Symposium IGARSS (1997), Vol. 2, pp. 869-871.
  16. F. K. Li and R. M. Goldstein, "Studies of multibaseline space borne interferometric synthetic aperture radars," IEEE Trans. Geosci. Remote Sensing 28, 88-97 (1990).
    [CrossRef]
  17. M. R. Foster and N. J. Guinzy, "The coefficient of coherence: Its estimation and use in geophysical data processing," Geophysics 32, 602-616 (1967).
    [CrossRef]
  18. R. Touzi, A. Lopes, J. Bruniquel, and P. W. Vachon, "Coherence estimation for SAR imagery," IEEE Trans. Geosci. Remote Sensing 37, 135-149 (1999).
    [CrossRef]
  19. P. B. G. Dammert, "Accuracy of INSAR measurements in forested areas," Proceedings of the ESA Workshop on Applications of European Space Agency, European Remote Sensing Satellites Interferometry FRINGE (1996), Vol. 1.
  20. A. M. Guarnieri and C. Prati, "SAR interferometry: a quick and dirty coherence estimator for data browsing," IEEE Trans. Geosci. Remote Sensing 35, 660-669 (1997).
    [CrossRef]
  21. G. Vasile, E. Trouvé, M. Ciuc, and V. Buzuloiu, "General adaptive neighborhood technique for improving SAR interferometric coherence estimation," J. Opt. Soc. Am. 21, 1455-1464 (2004).
    [CrossRef]
  22. C. López-Martínez and X. Fàbregas, "Polarimetric SAR Speckle Noise Model," IEEE Trans. Geosci. Remote Sensing 41, 2232-2242 (2003).
    [CrossRef]
  23. C. López-Martínez and E. Pottier, "Extended multilook multidimensional speckle noise model and its implications on the estimation of physical information," Proceedings of the International Geoscience and Remote Sensing Symposium IGARSS (2006).
  24. F. Gatelli, A. M. Guarnieru, F. Parizzi, C. Prati, and F. Rocca, "The wave number shift in SAR interferometry," IEEE Trans. Geosci. Remote Sensing 32, 855-865 (1994).
    [CrossRef]
  25. M. Seymour and I. Cumming, "Maximum likelihood estimation for SAR interferometry," Proceedings of the International Geoscience and Remote Sensing Symposium IGARSS (1994), Vol. 4, pp. 2272-2275.
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  27. J. O. Hagberg, L. M. H. Ulander, and J. Askne, "Repeat-pass interferometry over forested terrain," IEEE Trans. Geosci. Remote Sensing 33, 331-340 (1995).
    [CrossRef]
  28. C. López-Martínez, X. Fàbregas, and E. Pottier, "Wavelet transform based interferometric SAR coherence estimator," IEEE Signal Process. Lett. 12, 831-834 (2005).
    [CrossRef]
  29. E. Trouvé, M. Caramma, and H. Maître, "Fringe detection in noisy complex interferograms," Appl. Opt. 35, 3799-3806 (1996).
    [CrossRef] [PubMed]
  30. L. M. Novak and M. C. Burl, "Optimal speckle reduction polarimetric SAR imagery," IEEE Trans. Aerosp. Electron. Syst. 26, 293-305 (1990).
    [CrossRef]
  31. S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory (Prentice Hall, 1993).

2006 (1)

C. López-Martínez and E. Pottier, "Extended multilook multidimensional speckle noise model and its implications on the estimation of physical information," Proceedings of the International Geoscience and Remote Sensing Symposium IGARSS (2006).

2005 (2)

C. López-Martínez, X. Fàbregas, and E. Pottier, "Wavelet transform based interferometric SAR coherence estimator," IEEE Signal Process. Lett. 12, 831-834 (2005).
[CrossRef]

J. D. Ballester-Berman, J. M. Lopez-Sanchez, J. Fortuny-Guasch, "Retrieval of biophysical parameters of agricultural crops using polarimetric SAR interferometry," IEEE Trans. Geosci. Remote Sensing 43, 683-694 (2005).
[CrossRef]

2004 (3)

H. Wakabayashi, T. Matsuoka, K. Nakamura, and F. Nishio, "Polarimetric Characteristics of sea ice in the sea of Okhotsk observed by airborne L-band SAR," IEEE Trans. Geosci. Remote Sensing 42, 2412-2425 (2004).
[CrossRef]

M. E. Engdahl, J. T. Pulliainen, and M. T. Hallikainen, "Boreal forest coherence-based measures on interferometric pair suitability for operational stem volume retrieval," IEEE Geosci. Remote Sensing Lett. 1, 228-231 (2004).
[CrossRef]

G. Vasile, E. Trouvé, M. Ciuc, and V. Buzuloiu, "General adaptive neighborhood technique for improving SAR interferometric coherence estimation," J. Opt. Soc. Am. 21, 1455-1464 (2004).
[CrossRef]

2003 (3)

C. López-Martínez and X. Fàbregas, "Polarimetric SAR Speckle Noise Model," IEEE Trans. Geosci. Remote Sensing 41, 2232-2242 (2003).
[CrossRef]

J. P. Matthews, H. Kamada, S. Okuyama, Y. Yusa, and H. Shimizu, "Surface height adjustments in pyroclastic flow deposits observed at Unzen volcano by JERS-1 SAR interferometry," J. Volcanol. Geotherm. Res. 125, 247-270 (2003).
[CrossRef]

F. Mattia, T. Le Toan, J. S. Lee, and D. L. Schuler, "On the sensitivity of polarimetric coherence to small and large scale surface roughness," Proceedings of the International Geoscience and Remote Sensing Symposium IGARSS (2003), Vol. 2, pp. 690-692.

2002 (1)

D. H. Hoekman and M. J. Quiñones, "Biophysical forest type characterization in the Colombian Amazon by airborne polarimetric SAR," IEEE Trans. Geosci. Remote Sensing 40, 1288-1300 (2002).
[CrossRef]

2001 (1)

J. Weydahl, "Analysis of ERS tandem SAR coherence from glaciers, valleys, and fjords ice on Svalbard," IEEE Trans. Geosci. Remote Sensing 39, 2029-2039 (2001).
[CrossRef]

2000 (2)

J. Hyyppä, H. Hyyppä, M. Inkinena, M. Engdahla, S. Linkob, and Y. H. Zhuc, "Accuracy comparison of various remote sensing data sources in the retrieval of forest stand attributes," Forest Ecol. Manage. 128, 109-120 (2000).
[CrossRef]

E. W. Hoen and H. A. Zebker, "Topography-driven variations in backscatter strength and depth observed over the Greenland Ice Sheet with InSAR," Proceedings of the International Geoscience and Remote Sensing Symposium IGARSS (2000), Vol. 2, pp. 470-472.

1999 (1)

R. Touzi, A. Lopes, J. Bruniquel, and P. W. Vachon, "Coherence estimation for SAR imagery," IEEE Trans. Geosci. Remote Sensing 37, 135-149 (1999).
[CrossRef]

1998 (2)

S. R. Cloude and K. P. Papathanassiou, "Polarimetric SAR Interferometry," IEEE Trans. Geosci. Remote Sensing 36, 1551-1565 (1998).
[CrossRef]

R. Bamler and P. Hartl, "Synthetic aperture radar interferometry," Inverse Probl. 14, R1-R54 (1998).
[CrossRef]

1997 (3)

S. Li, C. Benson, L. Shapiro, and K. Dean, "Aufeis in the Ivishak from Satellite Radar River, Alaska, Interferometry Mapped," Remote Sens. Environ 20, 131-139 (1997).

A. M. Guarnieri and C. Prati, "SAR interferometry: a quick and dirty coherence estimator for data browsing," IEEE Trans. Geosci. Remote Sensing 35, 660-669 (1997).
[CrossRef]

A. Reigber and J. Moreira, "Phase unwrapping by fusion of local and global methods," Proceedings of the International Geoscience and Remote Sensing Symposium IGARSS (1997), Vol. 2, pp. 869-871.

1996 (1)

1995 (1)

J. O. Hagberg, L. M. H. Ulander, and J. Askne, "Repeat-pass interferometry over forested terrain," IEEE Trans. Geosci. Remote Sensing 33, 331-340 (1995).
[CrossRef]

1994 (2)

F. Gatelli, A. M. Guarnieru, F. Parizzi, C. Prati, and F. Rocca, "The wave number shift in SAR interferometry," IEEE Trans. Geosci. Remote Sensing 32, 855-865 (1994).
[CrossRef]

M. Seymour and I. Cumming, "Maximum likelihood estimation for SAR interferometry," Proceedings of the International Geoscience and Remote Sensing Symposium IGARSS (1994), Vol. 4, pp. 2272-2275.

1990 (2)

L. M. Novak and M. C. Burl, "Optimal speckle reduction polarimetric SAR imagery," IEEE Trans. Aerosp. Electron. Syst. 26, 293-305 (1990).
[CrossRef]

F. K. Li and R. M. Goldstein, "Studies of multibaseline space borne interferometric synthetic aperture radars," IEEE Trans. Geosci. Remote Sensing 28, 88-97 (1990).
[CrossRef]

1967 (1)

M. R. Foster and N. J. Guinzy, "The coefficient of coherence: Its estimation and use in geophysical data processing," Geophysics 32, 602-616 (1967).
[CrossRef]

Askne, J.

J. O. Hagberg, L. M. H. Ulander, and J. Askne, "Repeat-pass interferometry over forested terrain," IEEE Trans. Geosci. Remote Sensing 33, 331-340 (1995).
[CrossRef]

Ballester-Berman, J. D.

J. D. Ballester-Berman, J. M. Lopez-Sanchez, J. Fortuny-Guasch, "Retrieval of biophysical parameters of agricultural crops using polarimetric SAR interferometry," IEEE Trans. Geosci. Remote Sensing 43, 683-694 (2005).
[CrossRef]

Bamler, R.

R. Bamler and P. Hartl, "Synthetic aperture radar interferometry," Inverse Probl. 14, R1-R54 (1998).
[CrossRef]

Benson, C.

S. Li, C. Benson, L. Shapiro, and K. Dean, "Aufeis in the Ivishak from Satellite Radar River, Alaska, Interferometry Mapped," Remote Sens. Environ 20, 131-139 (1997).

Bruniquel, J.

R. Touzi, A. Lopes, J. Bruniquel, and P. W. Vachon, "Coherence estimation for SAR imagery," IEEE Trans. Geosci. Remote Sensing 37, 135-149 (1999).
[CrossRef]

Burl, M. C.

L. M. Novak and M. C. Burl, "Optimal speckle reduction polarimetric SAR imagery," IEEE Trans. Aerosp. Electron. Syst. 26, 293-305 (1990).
[CrossRef]

Buzuloiu, V.

G. Vasile, E. Trouvé, M. Ciuc, and V. Buzuloiu, "General adaptive neighborhood technique for improving SAR interferometric coherence estimation," J. Opt. Soc. Am. 21, 1455-1464 (2004).
[CrossRef]

Caramma, M.

Ciuc, M.

G. Vasile, E. Trouvé, M. Ciuc, and V. Buzuloiu, "General adaptive neighborhood technique for improving SAR interferometric coherence estimation," J. Opt. Soc. Am. 21, 1455-1464 (2004).
[CrossRef]

Cloude, S. R.

S. R. Cloude and K. P. Papathanassiou, "Polarimetric SAR Interferometry," IEEE Trans. Geosci. Remote Sensing 36, 1551-1565 (1998).
[CrossRef]

Cumming, I.

M. Seymour and I. Cumming, "Maximum likelihood estimation for SAR interferometry," Proceedings of the International Geoscience and Remote Sensing Symposium IGARSS (1994), Vol. 4, pp. 2272-2275.

Dammert, P. B. G.

P. B. G. Dammert, "Accuracy of INSAR measurements in forested areas," Proceedings of the ESA Workshop on Applications of European Space Agency, European Remote Sensing Satellites Interferometry FRINGE (1996), Vol. 1.

Dean, K.

S. Li, C. Benson, L. Shapiro, and K. Dean, "Aufeis in the Ivishak from Satellite Radar River, Alaska, Interferometry Mapped," Remote Sens. Environ 20, 131-139 (1997).

Engdahl, M. E.

M. E. Engdahl, J. T. Pulliainen, and M. T. Hallikainen, "Boreal forest coherence-based measures on interferometric pair suitability for operational stem volume retrieval," IEEE Geosci. Remote Sensing Lett. 1, 228-231 (2004).
[CrossRef]

Engdahla, M.

J. Hyyppä, H. Hyyppä, M. Inkinena, M. Engdahla, S. Linkob, and Y. H. Zhuc, "Accuracy comparison of various remote sensing data sources in the retrieval of forest stand attributes," Forest Ecol. Manage. 128, 109-120 (2000).
[CrossRef]

Fàbregas, X.

C. López-Martínez, X. Fàbregas, and E. Pottier, "Wavelet transform based interferometric SAR coherence estimator," IEEE Signal Process. Lett. 12, 831-834 (2005).
[CrossRef]

C. López-Martínez and X. Fàbregas, "Polarimetric SAR Speckle Noise Model," IEEE Trans. Geosci. Remote Sensing 41, 2232-2242 (2003).
[CrossRef]

Fortuny-Guasch, J.

J. D. Ballester-Berman, J. M. Lopez-Sanchez, J. Fortuny-Guasch, "Retrieval of biophysical parameters of agricultural crops using polarimetric SAR interferometry," IEEE Trans. Geosci. Remote Sensing 43, 683-694 (2005).
[CrossRef]

Foster, M. R.

M. R. Foster and N. J. Guinzy, "The coefficient of coherence: Its estimation and use in geophysical data processing," Geophysics 32, 602-616 (1967).
[CrossRef]

Gatelli, F.

F. Gatelli, A. M. Guarnieru, F. Parizzi, C. Prati, and F. Rocca, "The wave number shift in SAR interferometry," IEEE Trans. Geosci. Remote Sensing 32, 855-865 (1994).
[CrossRef]

Goldstein, R. M.

F. K. Li and R. M. Goldstein, "Studies of multibaseline space borne interferometric synthetic aperture radars," IEEE Trans. Geosci. Remote Sensing 28, 88-97 (1990).
[CrossRef]

Guarnieri, A. M.

A. M. Guarnieri and C. Prati, "SAR interferometry: a quick and dirty coherence estimator for data browsing," IEEE Trans. Geosci. Remote Sensing 35, 660-669 (1997).
[CrossRef]

Guarnieru, A. M.

F. Gatelli, A. M. Guarnieru, F. Parizzi, C. Prati, and F. Rocca, "The wave number shift in SAR interferometry," IEEE Trans. Geosci. Remote Sensing 32, 855-865 (1994).
[CrossRef]

Guinzy, N. J.

M. R. Foster and N. J. Guinzy, "The coefficient of coherence: Its estimation and use in geophysical data processing," Geophysics 32, 602-616 (1967).
[CrossRef]

Hagberg, J. O.

J. O. Hagberg, L. M. H. Ulander, and J. Askne, "Repeat-pass interferometry over forested terrain," IEEE Trans. Geosci. Remote Sensing 33, 331-340 (1995).
[CrossRef]

Hallikainen, M. T.

M. E. Engdahl, J. T. Pulliainen, and M. T. Hallikainen, "Boreal forest coherence-based measures on interferometric pair suitability for operational stem volume retrieval," IEEE Geosci. Remote Sensing Lett. 1, 228-231 (2004).
[CrossRef]

Hanssen, R. F.

R. F. Hanssen, Radar Interferometry (Kluwer Academic, 2001).

Hartl, P.

R. Bamler and P. Hartl, "Synthetic aperture radar interferometry," Inverse Probl. 14, R1-R54 (1998).
[CrossRef]

Hoekman, D. H.

D. H. Hoekman and M. J. Quiñones, "Biophysical forest type characterization in the Colombian Amazon by airborne polarimetric SAR," IEEE Trans. Geosci. Remote Sensing 40, 1288-1300 (2002).
[CrossRef]

Hoen, E. W.

E. W. Hoen and H. A. Zebker, "Topography-driven variations in backscatter strength and depth observed over the Greenland Ice Sheet with InSAR," Proceedings of the International Geoscience and Remote Sensing Symposium IGARSS (2000), Vol. 2, pp. 470-472.

Hyyppä, H.

J. Hyyppä, H. Hyyppä, M. Inkinena, M. Engdahla, S. Linkob, and Y. H. Zhuc, "Accuracy comparison of various remote sensing data sources in the retrieval of forest stand attributes," Forest Ecol. Manage. 128, 109-120 (2000).
[CrossRef]

Hyyppä, J.

J. Hyyppä, H. Hyyppä, M. Inkinena, M. Engdahla, S. Linkob, and Y. H. Zhuc, "Accuracy comparison of various remote sensing data sources in the retrieval of forest stand attributes," Forest Ecol. Manage. 128, 109-120 (2000).
[CrossRef]

Inkinena, M.

J. Hyyppä, H. Hyyppä, M. Inkinena, M. Engdahla, S. Linkob, and Y. H. Zhuc, "Accuracy comparison of various remote sensing data sources in the retrieval of forest stand attributes," Forest Ecol. Manage. 128, 109-120 (2000).
[CrossRef]

Kamada, H.

J. P. Matthews, H. Kamada, S. Okuyama, Y. Yusa, and H. Shimizu, "Surface height adjustments in pyroclastic flow deposits observed at Unzen volcano by JERS-1 SAR interferometry," J. Volcanol. Geotherm. Res. 125, 247-270 (2003).
[CrossRef]

Kasilingam, D.

D. Kasilingam, D. L. Schuler, J. S. Lee, and S. Malhotra, "Modulation of polarimetric coherence by ocean features," Proceedings of the International Geoscience and Remote Sensing Symposium IGARSS (2002), Vol. 1, pp. 432-434.

Kay, S. M.

S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory (Prentice Hall, 1993).

Le Toan, T.

F. Mattia, T. Le Toan, J. S. Lee, and D. L. Schuler, "On the sensitivity of polarimetric coherence to small and large scale surface roughness," Proceedings of the International Geoscience and Remote Sensing Symposium IGARSS (2003), Vol. 2, pp. 690-692.

Lee, J. S.

F. Mattia, T. Le Toan, J. S. Lee, and D. L. Schuler, "On the sensitivity of polarimetric coherence to small and large scale surface roughness," Proceedings of the International Geoscience and Remote Sensing Symposium IGARSS (2003), Vol. 2, pp. 690-692.

D. Kasilingam, D. L. Schuler, J. S. Lee, and S. Malhotra, "Modulation of polarimetric coherence by ocean features," Proceedings of the International Geoscience and Remote Sensing Symposium IGARSS (2002), Vol. 1, pp. 432-434.

Li, F. K.

F. K. Li and R. M. Goldstein, "Studies of multibaseline space borne interferometric synthetic aperture radars," IEEE Trans. Geosci. Remote Sensing 28, 88-97 (1990).
[CrossRef]

Li, S.

S. Li, C. Benson, L. Shapiro, and K. Dean, "Aufeis in the Ivishak from Satellite Radar River, Alaska, Interferometry Mapped," Remote Sens. Environ 20, 131-139 (1997).

Linkob, S.

J. Hyyppä, H. Hyyppä, M. Inkinena, M. Engdahla, S. Linkob, and Y. H. Zhuc, "Accuracy comparison of various remote sensing data sources in the retrieval of forest stand attributes," Forest Ecol. Manage. 128, 109-120 (2000).
[CrossRef]

Lopes, A.

R. Touzi, A. Lopes, J. Bruniquel, and P. W. Vachon, "Coherence estimation for SAR imagery," IEEE Trans. Geosci. Remote Sensing 37, 135-149 (1999).
[CrossRef]

López-Martínez, C.

C. López-Martínez and E. Pottier, "Extended multilook multidimensional speckle noise model and its implications on the estimation of physical information," Proceedings of the International Geoscience and Remote Sensing Symposium IGARSS (2006).

C. López-Martínez, X. Fàbregas, and E. Pottier, "Wavelet transform based interferometric SAR coherence estimator," IEEE Signal Process. Lett. 12, 831-834 (2005).
[CrossRef]

C. López-Martínez and X. Fàbregas, "Polarimetric SAR Speckle Noise Model," IEEE Trans. Geosci. Remote Sensing 41, 2232-2242 (2003).
[CrossRef]

Lopez-Sanchez, J. M.

J. D. Ballester-Berman, J. M. Lopez-Sanchez, J. Fortuny-Guasch, "Retrieval of biophysical parameters of agricultural crops using polarimetric SAR interferometry," IEEE Trans. Geosci. Remote Sensing 43, 683-694 (2005).
[CrossRef]

Maître, H.

Malhotra, S.

D. Kasilingam, D. L. Schuler, J. S. Lee, and S. Malhotra, "Modulation of polarimetric coherence by ocean features," Proceedings of the International Geoscience and Remote Sensing Symposium IGARSS (2002), Vol. 1, pp. 432-434.

Matsuoka, T.

H. Wakabayashi, T. Matsuoka, K. Nakamura, and F. Nishio, "Polarimetric Characteristics of sea ice in the sea of Okhotsk observed by airborne L-band SAR," IEEE Trans. Geosci. Remote Sensing 42, 2412-2425 (2004).
[CrossRef]

Matthews, J. P.

J. P. Matthews, H. Kamada, S. Okuyama, Y. Yusa, and H. Shimizu, "Surface height adjustments in pyroclastic flow deposits observed at Unzen volcano by JERS-1 SAR interferometry," J. Volcanol. Geotherm. Res. 125, 247-270 (2003).
[CrossRef]

Mattia, F.

F. Mattia, T. Le Toan, J. S. Lee, and D. L. Schuler, "On the sensitivity of polarimetric coherence to small and large scale surface roughness," Proceedings of the International Geoscience and Remote Sensing Symposium IGARSS (2003), Vol. 2, pp. 690-692.

Matzler, C.

T. Strozzi, U. Wegmuller, and C. Matzler, "Using repeat-pass SAR interferometry for mapping wet snow covers," Proceedings of the International Geoscience and Remote Sensing Symposium IGARSS (1998), Vol. 3, pp. 1650-1652.

Moreira, J.

A. Reigber and J. Moreira, "Phase unwrapping by fusion of local and global methods," Proceedings of the International Geoscience and Remote Sensing Symposium IGARSS (1997), Vol. 2, pp. 869-871.

Nakamura, K.

H. Wakabayashi, T. Matsuoka, K. Nakamura, and F. Nishio, "Polarimetric Characteristics of sea ice in the sea of Okhotsk observed by airborne L-band SAR," IEEE Trans. Geosci. Remote Sensing 42, 2412-2425 (2004).
[CrossRef]

Nishio, F.

H. Wakabayashi, T. Matsuoka, K. Nakamura, and F. Nishio, "Polarimetric Characteristics of sea ice in the sea of Okhotsk observed by airborne L-band SAR," IEEE Trans. Geosci. Remote Sensing 42, 2412-2425 (2004).
[CrossRef]

Novak, L. M.

L. M. Novak and M. C. Burl, "Optimal speckle reduction polarimetric SAR imagery," IEEE Trans. Aerosp. Electron. Syst. 26, 293-305 (1990).
[CrossRef]

Okuyama, S.

J. P. Matthews, H. Kamada, S. Okuyama, Y. Yusa, and H. Shimizu, "Surface height adjustments in pyroclastic flow deposits observed at Unzen volcano by JERS-1 SAR interferometry," J. Volcanol. Geotherm. Res. 125, 247-270 (2003).
[CrossRef]

Papathanassiou, K. P.

S. R. Cloude and K. P. Papathanassiou, "Polarimetric SAR Interferometry," IEEE Trans. Geosci. Remote Sensing 36, 1551-1565 (1998).
[CrossRef]

Parizzi, F.

F. Gatelli, A. M. Guarnieru, F. Parizzi, C. Prati, and F. Rocca, "The wave number shift in SAR interferometry," IEEE Trans. Geosci. Remote Sensing 32, 855-865 (1994).
[CrossRef]

Pottier, E.

C. López-Martínez and E. Pottier, "Extended multilook multidimensional speckle noise model and its implications on the estimation of physical information," Proceedings of the International Geoscience and Remote Sensing Symposium IGARSS (2006).

C. López-Martínez, X. Fàbregas, and E. Pottier, "Wavelet transform based interferometric SAR coherence estimator," IEEE Signal Process. Lett. 12, 831-834 (2005).
[CrossRef]

Prati, C.

A. M. Guarnieri and C. Prati, "SAR interferometry: a quick and dirty coherence estimator for data browsing," IEEE Trans. Geosci. Remote Sensing 35, 660-669 (1997).
[CrossRef]

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F. Mattia, T. Le Toan, J. S. Lee, and D. L. Schuler, "On the sensitivity of polarimetric coherence to small and large scale surface roughness," Proceedings of the International Geoscience and Remote Sensing Symposium IGARSS (2003), Vol. 2, pp. 690-692.

D. Kasilingam, D. L. Schuler, J. S. Lee, and S. Malhotra, "Modulation of polarimetric coherence by ocean features," Proceedings of the International Geoscience and Remote Sensing Symposium IGARSS (2002), Vol. 1, pp. 432-434.

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T. Strozzi, U. Wegmuller, and C. Matzler, "Using repeat-pass SAR interferometry for mapping wet snow covers," Proceedings of the International Geoscience and Remote Sensing Symposium IGARSS (1998), Vol. 3, pp. 1650-1652.

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J. Weydahl, "Analysis of ERS tandem SAR coherence from glaciers, valleys, and fjords ice on Svalbard," IEEE Trans. Geosci. Remote Sensing 39, 2029-2039 (2001).
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J. Hyyppä, H. Hyyppä, M. Inkinena, M. Engdahla, S. Linkob, and Y. H. Zhuc, "Accuracy comparison of various remote sensing data sources in the retrieval of forest stand attributes," Forest Ecol. Manage. 128, 109-120 (2000).
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[CrossRef]

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[CrossRef]

IEEE Signal Process. Lett. (1)

C. López-Martínez, X. Fàbregas, and E. Pottier, "Wavelet transform based interferometric SAR coherence estimator," IEEE Signal Process. Lett. 12, 831-834 (2005).
[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

C. López-Martínez and X. Fàbregas, "Polarimetric SAR Speckle Noise Model," IEEE Trans. Geosci. Remote Sensing 41, 2232-2242 (2003).
[CrossRef]

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[CrossRef]

J. Weydahl, "Analysis of ERS tandem SAR coherence from glaciers, valleys, and fjords ice on Svalbard," IEEE Trans. Geosci. Remote Sensing 39, 2029-2039 (2001).
[CrossRef]

R. Touzi, A. Lopes, J. Bruniquel, and P. W. Vachon, "Coherence estimation for SAR imagery," IEEE Trans. Geosci. Remote Sensing 37, 135-149 (1999).
[CrossRef]

A. M. Guarnieri and C. Prati, "SAR interferometry: a quick and dirty coherence estimator for data browsing," IEEE Trans. Geosci. Remote Sensing 35, 660-669 (1997).
[CrossRef]

H. Wakabayashi, T. Matsuoka, K. Nakamura, and F. Nishio, "Polarimetric Characteristics of sea ice in the sea of Okhotsk observed by airborne L-band SAR," IEEE Trans. Geosci. Remote Sensing 42, 2412-2425 (2004).
[CrossRef]

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[CrossRef]

J. Volcanol. Geotherm. Res. (1)

J. P. Matthews, H. Kamada, S. Okuyama, Y. Yusa, and H. Shimizu, "Surface height adjustments in pyroclastic flow deposits observed at Unzen volcano by JERS-1 SAR interferometry," J. Volcanol. Geotherm. Res. 125, 247-270 (2003).
[CrossRef]

Remote Sens. Environ (1)

S. Li, C. Benson, L. Shapiro, and K. Dean, "Aufeis in the Ivishak from Satellite Radar River, Alaska, Interferometry Mapped," Remote Sens. Environ 20, 131-139 (1997).

Other (10)

F. Mattia, T. Le Toan, J. S. Lee, and D. L. Schuler, "On the sensitivity of polarimetric coherence to small and large scale surface roughness," Proceedings of the International Geoscience and Remote Sensing Symposium IGARSS (2003), Vol. 2, pp. 690-692.

D. Kasilingam, D. L. Schuler, J. S. Lee, and S. Malhotra, "Modulation of polarimetric coherence by ocean features," Proceedings of the International Geoscience and Remote Sensing Symposium IGARSS (2002), Vol. 1, pp. 432-434.

E. W. Hoen and H. A. Zebker, "Topography-driven variations in backscatter strength and depth observed over the Greenland Ice Sheet with InSAR," Proceedings of the International Geoscience and Remote Sensing Symposium IGARSS (2000), Vol. 2, pp. 470-472.

T. Strozzi, U. Wegmuller, and C. Matzler, "Using repeat-pass SAR interferometry for mapping wet snow covers," Proceedings of the International Geoscience and Remote Sensing Symposium IGARSS (1998), Vol. 3, pp. 1650-1652.

P. B. G. Dammert, "Accuracy of INSAR measurements in forested areas," Proceedings of the ESA Workshop on Applications of European Space Agency, European Remote Sensing Satellites Interferometry FRINGE (1996), Vol. 1.

A. Reigber and J. Moreira, "Phase unwrapping by fusion of local and global methods," Proceedings of the International Geoscience and Remote Sensing Symposium IGARSS (1997), Vol. 2, pp. 869-871.

M. Seymour and I. Cumming, "Maximum likelihood estimation for SAR interferometry," Proceedings of the International Geoscience and Remote Sensing Symposium IGARSS (1994), Vol. 4, pp. 2272-2275.

R. F. Hanssen, Radar Interferometry (Kluwer Academic, 2001).

C. López-Martínez and E. Pottier, "Extended multilook multidimensional speckle noise model and its implications on the estimation of physical information," Proceedings of the International Geoscience and Remote Sensing Symposium IGARSS (2006).

S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory (Prentice Hall, 1993).

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Figures (10)

Fig. 1
Fig. 1

True and estimated speckle biases of coherence.

Fig. 2
Fig. 2

Algorithm for speckle bias reduction in coherence estimation.

Fig. 3
Fig. 3

Variation for the reduction of biases due to systematic phase variations.

Fig. 4
Fig. 4

(Left) Mean and (right) MSE values of the estimated coherence values with the multilook algorithm ( | ρ M L T | ) and the algorithm for the speckle bias reduction ( | ρ N B S | ) .

Fig. 5
Fig. 5

(Left) Mean and (right) MSE values of the estimated coherence values with the multilook algorithm ( | ρ M L T | ) and the algorithm for the speckle bias reduction ( | ρ N B S | ) .

Fig. 6
Fig. 6

Mean and standard deviation values of the estimated coherence values with the multilook algorithm ( | ρ M L T | ) and the algorithm for the speckle bias reduction ( | ρ N B S | ) with a 7 × 7 looks window. Topography is not estimated from data, but offered as an input to the algorithm.

Fig. 7
Fig. 7

Histograms of coherence for the Traunstein image.

Fig. 8
Fig. 8

Original and nonbiased estimated coherences based on 3 × 3 pixel windows.

Fig. 9
Fig. 9

ERS-1 and ERS-2 tandem interferogram: (a) phase ϕ, (b) coherence histograms, (c) | ρ M L T | , (d) | ρ N B S | . Coherences are obtained with 7 × 7 pixel averaging windows.

Fig. 10
Fig. 10

Value of the term | ρ | N c z ¯ n .

Tables (1)

Tables Icon

Table 1 Mean Coherence Values for the Areas of Fig. 8

Equations (57)

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| ρ | = | ρ e j ϕ x | = | E { S 1 S 2 * } | E { | S 1 | 2 } E { | S 2 | 2 } ,
| ρ M L T | = | m = 1 M n = 1 N S 1 ( m , n ) S 2 * ( m , n ) | m = 1 M n = 1 N | S 1 ( m , n ) | 2 m = 1 M n = 1 N | S 2 ( m , n ) | 2 ,
| ρ P H C DEM | = | m = 1 M n = 1 N S 1 ( m , n ) S 2 * ( m , n ) e j ϕ x | m = 1 M n = 1 N | S 1 ( m , n ) | 2 m = 1 M n = 1 N | S 2 ( m , n ) | 2 .
| ρ P H C model | = max φ x | m = 1 M n = 1 N S 1 ( m , n ) S 2 * ( m , n ) e j f ( φ x ) | m = 1 M n = 1 N | S 1 ( m , n ) | 2 m = 1 M n = 1 N | S 2 ( m , n ) | 2 ,
R I N T = m = 1 M n = 1 N | S 1 ( m , n ) | 2 | S 2 ( m , n ) | 2 m = 1 M n = 1 N | S 1 ( m , n ) | 4 m = 1 M n = 1 N | S 2 ( m , n ) | 4 ,
| ρ I N T | = { 2 R I N T 1 R I N T > 1 / 2 0 R I N T 1 / 2 .
S 1 S 2 * = | S 1 S 2 * | e j ( ϕ 1 ϕ 2 ) = z e j ϕ ,
S 1 S 2 * n = ψ n m exp ( j ϕ x ) Multiplicative   term + ψ ( | ρ | N c z ¯ n ) exp ( j ϕ x ) + ψ ( n a r + j n a i ) Additive   term ,
ψ = E { | S i | 2 } E { | S j | 2 } .
N c = Γ ( n + ) Γ ( ) Γ ( n ) | ρ | 2 F 1 ( 3 2 n , 1 2 ; 2 ; | ρ | 2 ) .
E { n m } = N c z ¯ n ,
σ n m 2 = N c 2 ( 1 + | ρ | 2 ) 2 n .
E { n a r } = E { n a i } = 0 ,
σ n a r 2 = σ n a i 2 = 1 2 n ( 1 | ρ | 2 ) 1.32 n .
ϕ x ( m , n ) = 2 π s x m + 2 π s y n + ϕ x 0 ,
ω x = 2 π s x ,
ω y = 2 π s y .
h ( m , n ) = 1 M N p = 1 M q = 1 N δ ( p m ) δ ( q n ) ,
H ( ω x , ω y ) = 1 M sin ( M 2 ω x ) sin ( ω x 2 ) 1 N sin ( N 2 ω y ) sin ( ω y 2 ) ,
u 1 ( x , y ) = ψ n m exp ( j ϕ x ( x , y ) ) ,
r u 1 u 1 ( k , l ) = ψ 2 N c 2 [ z ¯ n 2 + ( 1 + | ρ | 2 ) 2 n δ ( k , l ) ] × e j [ ( 2 π / s x ) k + ( 2 π / s y ) l ] ,
S u 1 u 1 ( ω x , ω y ) = ψ 2 N c 2 ( 1 + | ρ | 2 ) 2 n + ψ 2 N c 2 z ¯ n 2 ( 2 π ) 2 × δ ( ω x 2 π s x ) δ ( ω y 2 π s y ) .
S v 1 v 1 ( ω x , ω y ) = ψ 2 N c 2 ( 1 + | ρ | 2 ) 2 n × | 1 M sin ( M 2 ω x ) sin ( ω x 2 ) 1 N sin ( N 2 ω y ) sin ( ω y 2 ) | 2 + ψ 2 N c 2 z ¯ n 2 ( 2 π ) 2 Δ 2 δ ( ω x 2 π s x ) δ ( ω y 2 π s y ) ,
Δ = | 1 M sin ( M π s x ) sin ( π s x ) 1 N sin ( N π s y ) sin ( π s y ) | .
r v 1 v 1 ( k , l ) = ψ 2 N c 2 z ¯ n 2 Δ 2 e j [ ( 2 π / s x ) k + ( 2 π / s y ) l ] + ψ 2 N c 2 ( 1 + | ρ | 2 ) 2 n 1 M k ( ( M 1 ) , ( M 1 ) ) 1 N l ( ( N 1 ) , ( N 1 ) ) ,
v 1 ( x , y ) = ψ Δ exp ( j ϕ x ( x , y ) ) n m ( x , y ) ,
E { n m } = N c z ¯ n ,
σ n m 2 = N c 2 ( 1 + | ρ | 2 ) 2 n M N .
u 2 ( x , y ) = ψ ( | ρ | N c z ¯ n ) exp [ j ϕ x ( x , y ) ] ,
v 2 ( x , y ) = ψ Δ ( | ρ | N c z ¯ n ) exp [ j ϕ x ( x , y ) ] .
u 3 ( x , y ) = ψ ( n a r ( x , y ) + j n a i ( x , y ) ) .
r { u 3 } { u 3 } ( k , l ) = ψ 1 2 n ( 1 | ρ | 2 ) 1.32 n δ ( k , l ) ,
S { u 3 } { u 3 } ( ω x , ω y ) = ψ 1 2 n ( 1 | ρ | 2 ) 1.32 n .
S { v 3 } { v 3 } ( ω x , ω y ) = 1 2 n M N ( 1 | ρ | 2 ) 1.32 n N M × | 1 M sin ( M 2 ω x ) sin ( ω x 2 ) 1 N sin ( N 2 ω y ) sin ( ω y 2 ) | 2 ,
r { v 3 } { v 3 } ( k , l ) = 1 2 n N M ( 1 | ρ | 2 ) 1.32 n N M 1 M k [ ( M 1 ) , ( M 1 ) ] 1 N l [ ( N 1 ) , ( N 1 ) ] .
v 3 ( x , y ) = ψ [ n a r ( x , y ) + j n a i ( x , y ) ] ,
E { n a r } = E { n a i } = 0 ,
σ n a r 2 = σ n a i 2 = 1 2 n M N ( 1 | ρ | 2 ) 1.32 n M N .
S 1 S 2 * n M N = ψ Δ n m exp ( j ϕ x ) + ψ Δ ( | ρ | N c z ¯ n ) exp ( j ϕ x ) + ψ ( n a r + j n a i ) .
E { S 1 S 2 * n M N } = ψ Δ E { n m } exp ( j ϕ x ) + ψ Δ ( | ρ | N c z ¯ n ) × exp ( j ϕ x ) = ψ Δ N c z ¯ n exp ( j ϕ x ) + ψ Δ ( | ρ | N c z ¯ n ) × exp ( j ϕ x ) = ψ Δ | ρ | exp ( j ϕ x ) .
S 1 S 2 * M N = ψ Δ n m exp ( j ϕ x ) + ψ Δ ( | ρ | N c z ¯ n ) exp ( j ϕ x ) + ψ ( n a r + j n a i ) .
E { | S 1 | 2 M N | S 2 | 2 M N } = ψ ( 1 + | ρ | 2 M N ) .
| S 1 | 2 M N | S 2 | 2 M N ψ ( 1 + 1 M N ) ,
ρ M L T = Δ n m exp ( j ϕ x ) + Δ ( | ρ | N c z ¯ n ) exp ( j ϕ x ) + ( n a r + j n a i ) ( 1 + 1 M N ) .
ρ M L T | ρ | Δ exp ( j ϕ x ) + ( 1 + 1 M N ) 1 / 2 ( n a r + j n a i ) ,
E { | ρ M L T | 2 } | ρ | 2 Δ 2 + ( 1 + 1 M N ) 1 1 M N ( 1 | ρ | 2 ) 1.32 M N .
Δ speckle 2 = ( 1 + 1 M N ) 1 1 M N ( 1 | ρ | 2 ) 1.32 M N ,
| ρ M L T | 2 | ρ N B S | 2 Δ 2 + 1 M N ( 1 | ρ N B S | 2 ) .
| ρ N B S | 2 ( | ρ M L T | 2 1 M N ) ( M N M N Δ 2 1 ) .
MSE ( | ρ ^ | ) = E { ( | ρ ^ | | ρ | ) 2 } = var { | ρ ^ | } + b 2 { | ρ ^ | } ,
u 1 ( x , y ) = ψ n m exp ( j ϕ x ) ,
r u 1 u 1 ( k , l ) = m = n = u 1 * ( m , n ) u 1 ( m + k , n + l ) = ψ 2 exp [ j ( 2 π s x k + 2 π s y l ) ] m = n = n m * ( m , n ) × n m ( m + k , n + l ) = ψ 2 exp [ j ( 2 π s x k + 2 π s y l ) ] r n m n m ( k , l ) .
r n m n m ( k , l ) = N c 2 [ z ¯ n 2 + ( 1 + | ρ | 2 ) 2 n δ ( k , l ) ] ,
r n m n m ( k , l ) | n = 1 = N c 2 z ¯ n 2 [ 1 + δ ( k , l ) ] .
S u 1 u 1 ( ω x , ω y ) = k = l = r u 1 u 1 ( k , l ) exp ( j ω x k ) exp ( j ω y l ) = ψ 2 k = l = N c 2 ( 1 + | ρ | 2 ) 2 n δ ( k , l ) + ψ 2 N c 2 z ¯ n 2 k = l = exp { j [ ( ω x 2 π s x ) k + ( ω y 2 π s y ) l ] } ,
ρ M L T = Δ n m exp ( j ϕ x ) ( 1 + 1 M N ) + Δ ( | ρ | N c z ¯ n ) exp ( j ϕ x ) ( 1 + 1 M N ) + ( n a r + j n a i ) ( 1 + 1 M N ) .
Δ n m exp ( j ϕ x ) ( 1 + 1 M N ) M N > 1 Δ | ρ | exp ( j ϕ x ) ,

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