Abstract

We present a Wiener filter that is especially suitable for speckle and noise reduction in multilook synthetic aperture radar (SAR) imagery. The proposed filter is nonparametric, not being based on parametrized analytical models of signal statistics. Instead, the Wiener–Hopf equation is expressed entirely in terms of observed signal statistics, with no reference to the possibly unobservable pure signal and noise. This Wiener filter is simple in concept and implementation, exactly minimum mean-square error, and directly applicable to signal-dependent and multiplicative noise. We demonstrate the filtering of a genuine two-look SAR image and show how a nonnegatively constrained version of the filter substantially reduces ringing.

© 2000 Optical Society of America

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  1. R. Caprari, “Non-parametric Wiener filter for reducing noise on reproducible pure signals,” J. Phys. A 32, 3075–3094 (1999).
    [CrossRef]
  2. C. Oliver, S. Quegan, Understanding Synthetic Aperture Radar Images (Artech House, Boston, 1998).
  3. K. Rank, M. Lendl, R. Unbehauen, “Estimation of image noise variance,” IEE Proc. Vision Image Signal Process. 146, 80–84 (1999).
    [CrossRef]
  4. I. Birrer, E. Bracalente, G. Dome, J. Sweet, G. Berthold, “σ0 signature of the Amazon rain forest obtained from the Seasat scatterometer,” IEEE Trans. Geosci. Remote Sens. 20, 11–17 (1982).
    [CrossRef]
  5. D. Early, D. Long, “Azimuthal modulation of C-band scatterometer σ0 over southern ocean sea ice,” IEEE Trans. Geosci. Remote Sens. 35, 1201–1209 (1997).
    [CrossRef]
  6. J. Goodman, “Some fundamental properties of speckle,” J. Opt. Soc. Am. 66, 1145–1150 (1976).
    [CrossRef]
  7. J. Goodman, “A random walk through the field of speckle,” Opt. Eng. 86, 610–612 (1986).
  8. L. Porcello, N. Massey, R. Innes, J. Marks, “Speckle reduction in synthetic aperture radars,” J. Opt. Soc. Am. 66, 1305–1311 (1976).
    [CrossRef]
  9. F.-L. Li, C. Croft, D. Held, “Comparison of several techniques to obtain multiple-look SAR imagery,” IEEE Trans. Geosci. Remote Sens. 21, 370–375 (1983).
    [CrossRef]
  10. C. Helstrom, “Image restoration by the method of least squares,” J. Opt. Soc. Am. 57, 297–303 (1967).
    [CrossRef]
  11. S. Reichenbach, S. Park, “Small convolution kernels for high-fidelity image restoration,” IEEE Trans. Signal Process. 39, 2263–2274 (1991).
    [CrossRef]
  12. V. Frost, J. Stiles, K. Shanmugan, J. Holtzman, “A model for radar images and its application to adaptive digital filtering of multiplicative noise,” IEEE Trans. Pattern Anal. Mach. Intell. 4, 157–166 (1982).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  15. N. Stacy, M. Burgess, M. Muller, R. Smith, “Ingara: an integrated airborne imaging radar system,” in Proceedings of the International Geoscience and Remote Sensing Symposium (Institute of Electrical and Electronics Engineers, New York, 1996), Vol. 3, pp. 1618–1620.
  16. S.-S. Jiang, A. Sawchuk, “Noise updating repeated Wiener filter and other adaptive noise smoothing filters using local image statistics,” Appl. Opt. 25, 2326–2337 (1986).
    [CrossRef] [PubMed]
  17. R. Lagendijk, J. Biemond, D. Boekee, “Regularized iterative image restoration with ringing reduction,” IEEE Trans. Acoust. Speech Signal Process. 36, 1874–1888 (1988).
    [CrossRef]
  18. A. Tekalp, H. Kaufman, J. Woods, “Edge-adaptive Kalman filtering for image restoration with ringing suppression,” IEEE Trans. Acoust. Speech Signal Process. 37, 892–899 (1989).
    [CrossRef]
  19. Y. Cao, P. Eggermont, S. Terebey, “Cross Burg entropy maximization and its application to ringing suppression in image reconstruction,” IEEE Trans. Image Process. 8, 286–292 (1999).
    [CrossRef]
  20. R. Caprari, “Generalized matched filters and univariate Neyman–Pearson detectors for image target detection,” IEEE Trans. Inform. Theory 46, 1932–1937 (2000).
    [CrossRef]

2000

R. Caprari, “Generalized matched filters and univariate Neyman–Pearson detectors for image target detection,” IEEE Trans. Inform. Theory 46, 1932–1937 (2000).
[CrossRef]

1999

Y. Cao, P. Eggermont, S. Terebey, “Cross Burg entropy maximization and its application to ringing suppression in image reconstruction,” IEEE Trans. Image Process. 8, 286–292 (1999).
[CrossRef]

R. Caprari, “Non-parametric Wiener filter for reducing noise on reproducible pure signals,” J. Phys. A 32, 3075–3094 (1999).
[CrossRef]

K. Rank, M. Lendl, R. Unbehauen, “Estimation of image noise variance,” IEE Proc. Vision Image Signal Process. 146, 80–84 (1999).
[CrossRef]

1997

D. Early, D. Long, “Azimuthal modulation of C-band scatterometer σ0 over southern ocean sea ice,” IEEE Trans. Geosci. Remote Sens. 35, 1201–1209 (1997).
[CrossRef]

1995

1991

S. Reichenbach, S. Park, “Small convolution kernels for high-fidelity image restoration,” IEEE Trans. Signal Process. 39, 2263–2274 (1991).
[CrossRef]

1990

1989

A. Tekalp, H. Kaufman, J. Woods, “Edge-adaptive Kalman filtering for image restoration with ringing suppression,” IEEE Trans. Acoust. Speech Signal Process. 37, 892–899 (1989).
[CrossRef]

1988

R. Lagendijk, J. Biemond, D. Boekee, “Regularized iterative image restoration with ringing reduction,” IEEE Trans. Acoust. Speech Signal Process. 36, 1874–1888 (1988).
[CrossRef]

1986

1983

F.-L. Li, C. Croft, D. Held, “Comparison of several techniques to obtain multiple-look SAR imagery,” IEEE Trans. Geosci. Remote Sens. 21, 370–375 (1983).
[CrossRef]

1982

I. Birrer, E. Bracalente, G. Dome, J. Sweet, G. Berthold, “σ0 signature of the Amazon rain forest obtained from the Seasat scatterometer,” IEEE Trans. Geosci. Remote Sens. 20, 11–17 (1982).
[CrossRef]

V. Frost, J. Stiles, K. Shanmugan, J. Holtzman, “A model for radar images and its application to adaptive digital filtering of multiplicative noise,” IEEE Trans. Pattern Anal. Mach. Intell. 4, 157–166 (1982).
[CrossRef] [PubMed]

1976

1967

April, G.

Berthold, G.

I. Birrer, E. Bracalente, G. Dome, J. Sweet, G. Berthold, “σ0 signature of the Amazon rain forest obtained from the Seasat scatterometer,” IEEE Trans. Geosci. Remote Sens. 20, 11–17 (1982).
[CrossRef]

Biemond, J.

R. Lagendijk, J. Biemond, D. Boekee, “Regularized iterative image restoration with ringing reduction,” IEEE Trans. Acoust. Speech Signal Process. 36, 1874–1888 (1988).
[CrossRef]

Birrer, I.

I. Birrer, E. Bracalente, G. Dome, J. Sweet, G. Berthold, “σ0 signature of the Amazon rain forest obtained from the Seasat scatterometer,” IEEE Trans. Geosci. Remote Sens. 20, 11–17 (1982).
[CrossRef]

Boekee, D.

R. Lagendijk, J. Biemond, D. Boekee, “Regularized iterative image restoration with ringing reduction,” IEEE Trans. Acoust. Speech Signal Process. 36, 1874–1888 (1988).
[CrossRef]

Bracalente, E.

I. Birrer, E. Bracalente, G. Dome, J. Sweet, G. Berthold, “σ0 signature of the Amazon rain forest obtained from the Seasat scatterometer,” IEEE Trans. Geosci. Remote Sens. 20, 11–17 (1982).
[CrossRef]

Burgess, M.

N. Stacy, M. Burgess, M. Muller, R. Smith, “Ingara: an integrated airborne imaging radar system,” in Proceedings of the International Geoscience and Remote Sensing Symposium (Institute of Electrical and Electronics Engineers, New York, 1996), Vol. 3, pp. 1618–1620.

Cao, Y.

Y. Cao, P. Eggermont, S. Terebey, “Cross Burg entropy maximization and its application to ringing suppression in image reconstruction,” IEEE Trans. Image Process. 8, 286–292 (1999).
[CrossRef]

Caprari, R.

R. Caprari, “Generalized matched filters and univariate Neyman–Pearson detectors for image target detection,” IEEE Trans. Inform. Theory 46, 1932–1937 (2000).
[CrossRef]

R. Caprari, “Non-parametric Wiener filter for reducing noise on reproducible pure signals,” J. Phys. A 32, 3075–3094 (1999).
[CrossRef]

Croft, C.

F.-L. Li, C. Croft, D. Held, “Comparison of several techniques to obtain multiple-look SAR imagery,” IEEE Trans. Geosci. Remote Sens. 21, 370–375 (1983).
[CrossRef]

Dome, G.

I. Birrer, E. Bracalente, G. Dome, J. Sweet, G. Berthold, “σ0 signature of the Amazon rain forest obtained from the Seasat scatterometer,” IEEE Trans. Geosci. Remote Sens. 20, 11–17 (1982).
[CrossRef]

Early, D.

D. Early, D. Long, “Azimuthal modulation of C-band scatterometer σ0 over southern ocean sea ice,” IEEE Trans. Geosci. Remote Sens. 35, 1201–1209 (1997).
[CrossRef]

Eggermont, P.

Y. Cao, P. Eggermont, S. Terebey, “Cross Burg entropy maximization and its application to ringing suppression in image reconstruction,” IEEE Trans. Image Process. 8, 286–292 (1999).
[CrossRef]

Franceschetti, G.

Frost, V.

V. Frost, J. Stiles, K. Shanmugan, J. Holtzman, “A model for radar images and its application to adaptive digital filtering of multiplicative noise,” IEEE Trans. Pattern Anal. Mach. Intell. 4, 157–166 (1982).
[CrossRef] [PubMed]

Goodman, J.

J. Goodman, “A random walk through the field of speckle,” Opt. Eng. 86, 610–612 (1986).

J. Goodman, “Some fundamental properties of speckle,” J. Opt. Soc. Am. 66, 1145–1150 (1976).
[CrossRef]

Harvey, E.

Held, D.

F.-L. Li, C. Croft, D. Held, “Comparison of several techniques to obtain multiple-look SAR imagery,” IEEE Trans. Geosci. Remote Sens. 21, 370–375 (1983).
[CrossRef]

Helstrom, C.

Holtzman, J.

V. Frost, J. Stiles, K. Shanmugan, J. Holtzman, “A model for radar images and its application to adaptive digital filtering of multiplicative noise,” IEEE Trans. Pattern Anal. Mach. Intell. 4, 157–166 (1982).
[CrossRef] [PubMed]

Innes, R.

Jiang, S.-S.

Kaufman, H.

A. Tekalp, H. Kaufman, J. Woods, “Edge-adaptive Kalman filtering for image restoration with ringing suppression,” IEEE Trans. Acoust. Speech Signal Process. 37, 892–899 (1989).
[CrossRef]

Lagendijk, R.

R. Lagendijk, J. Biemond, D. Boekee, “Regularized iterative image restoration with ringing reduction,” IEEE Trans. Acoust. Speech Signal Process. 36, 1874–1888 (1988).
[CrossRef]

Lendl, M.

K. Rank, M. Lendl, R. Unbehauen, “Estimation of image noise variance,” IEE Proc. Vision Image Signal Process. 146, 80–84 (1999).
[CrossRef]

Li, F.-L.

F.-L. Li, C. Croft, D. Held, “Comparison of several techniques to obtain multiple-look SAR imagery,” IEEE Trans. Geosci. Remote Sens. 21, 370–375 (1983).
[CrossRef]

Long, D.

D. Early, D. Long, “Azimuthal modulation of C-band scatterometer σ0 over southern ocean sea ice,” IEEE Trans. Geosci. Remote Sens. 35, 1201–1209 (1997).
[CrossRef]

Marks, J.

Massey, N.

Muller, M.

N. Stacy, M. Burgess, M. Muller, R. Smith, “Ingara: an integrated airborne imaging radar system,” in Proceedings of the International Geoscience and Remote Sensing Symposium (Institute of Electrical and Electronics Engineers, New York, 1996), Vol. 3, pp. 1618–1620.

Oliver, C.

C. Oliver, S. Quegan, Understanding Synthetic Aperture Radar Images (Artech House, Boston, 1998).

Park, S.

S. Reichenbach, S. Park, “Small convolution kernels for high-fidelity image restoration,” IEEE Trans. Signal Process. 39, 2263–2274 (1991).
[CrossRef]

Pascazio, V.

Porcello, L.

Quegan, S.

C. Oliver, S. Quegan, Understanding Synthetic Aperture Radar Images (Artech House, Boston, 1998).

Rank, K.

K. Rank, M. Lendl, R. Unbehauen, “Estimation of image noise variance,” IEE Proc. Vision Image Signal Process. 146, 80–84 (1999).
[CrossRef]

Reichenbach, S.

S. Reichenbach, S. Park, “Small convolution kernels for high-fidelity image restoration,” IEEE Trans. Signal Process. 39, 2263–2274 (1991).
[CrossRef]

Sawchuk, A.

Schirinzi, G.

Shanmugan, K.

V. Frost, J. Stiles, K. Shanmugan, J. Holtzman, “A model for radar images and its application to adaptive digital filtering of multiplicative noise,” IEEE Trans. Pattern Anal. Mach. Intell. 4, 157–166 (1982).
[CrossRef] [PubMed]

Smith, R.

N. Stacy, M. Burgess, M. Muller, R. Smith, “Ingara: an integrated airborne imaging radar system,” in Proceedings of the International Geoscience and Remote Sensing Symposium (Institute of Electrical and Electronics Engineers, New York, 1996), Vol. 3, pp. 1618–1620.

Stacy, N.

N. Stacy, M. Burgess, M. Muller, R. Smith, “Ingara: an integrated airborne imaging radar system,” in Proceedings of the International Geoscience and Remote Sensing Symposium (Institute of Electrical and Electronics Engineers, New York, 1996), Vol. 3, pp. 1618–1620.

Stiles, J.

V. Frost, J. Stiles, K. Shanmugan, J. Holtzman, “A model for radar images and its application to adaptive digital filtering of multiplicative noise,” IEEE Trans. Pattern Anal. Mach. Intell. 4, 157–166 (1982).
[CrossRef] [PubMed]

Sweet, J.

I. Birrer, E. Bracalente, G. Dome, J. Sweet, G. Berthold, “σ0 signature of the Amazon rain forest obtained from the Seasat scatterometer,” IEEE Trans. Geosci. Remote Sens. 20, 11–17 (1982).
[CrossRef]

Tekalp, A.

A. Tekalp, H. Kaufman, J. Woods, “Edge-adaptive Kalman filtering for image restoration with ringing suppression,” IEEE Trans. Acoust. Speech Signal Process. 37, 892–899 (1989).
[CrossRef]

Terebey, S.

Y. Cao, P. Eggermont, S. Terebey, “Cross Burg entropy maximization and its application to ringing suppression in image reconstruction,” IEEE Trans. Image Process. 8, 286–292 (1999).
[CrossRef]

Unbehauen, R.

K. Rank, M. Lendl, R. Unbehauen, “Estimation of image noise variance,” IEE Proc. Vision Image Signal Process. 146, 80–84 (1999).
[CrossRef]

Woods, J.

A. Tekalp, H. Kaufman, J. Woods, “Edge-adaptive Kalman filtering for image restoration with ringing suppression,” IEEE Trans. Acoust. Speech Signal Process. 37, 892–899 (1989).
[CrossRef]

Appl. Opt.

IEE Proc. Vision Image Signal Process.

K. Rank, M. Lendl, R. Unbehauen, “Estimation of image noise variance,” IEE Proc. Vision Image Signal Process. 146, 80–84 (1999).
[CrossRef]

IEEE Trans. Acoust. Speech Signal Process.

R. Lagendijk, J. Biemond, D. Boekee, “Regularized iterative image restoration with ringing reduction,” IEEE Trans. Acoust. Speech Signal Process. 36, 1874–1888 (1988).
[CrossRef]

A. Tekalp, H. Kaufman, J. Woods, “Edge-adaptive Kalman filtering for image restoration with ringing suppression,” IEEE Trans. Acoust. Speech Signal Process. 37, 892–899 (1989).
[CrossRef]

IEEE Trans. Geosci. Remote Sens.

I. Birrer, E. Bracalente, G. Dome, J. Sweet, G. Berthold, “σ0 signature of the Amazon rain forest obtained from the Seasat scatterometer,” IEEE Trans. Geosci. Remote Sens. 20, 11–17 (1982).
[CrossRef]

D. Early, D. Long, “Azimuthal modulation of C-band scatterometer σ0 over southern ocean sea ice,” IEEE Trans. Geosci. Remote Sens. 35, 1201–1209 (1997).
[CrossRef]

F.-L. Li, C. Croft, D. Held, “Comparison of several techniques to obtain multiple-look SAR imagery,” IEEE Trans. Geosci. Remote Sens. 21, 370–375 (1983).
[CrossRef]

IEEE Trans. Image Process.

Y. Cao, P. Eggermont, S. Terebey, “Cross Burg entropy maximization and its application to ringing suppression in image reconstruction,” IEEE Trans. Image Process. 8, 286–292 (1999).
[CrossRef]

IEEE Trans. Inform. Theory

R. Caprari, “Generalized matched filters and univariate Neyman–Pearson detectors for image target detection,” IEEE Trans. Inform. Theory 46, 1932–1937 (2000).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell.

V. Frost, J. Stiles, K. Shanmugan, J. Holtzman, “A model for radar images and its application to adaptive digital filtering of multiplicative noise,” IEEE Trans. Pattern Anal. Mach. Intell. 4, 157–166 (1982).
[CrossRef] [PubMed]

IEEE Trans. Signal Process.

S. Reichenbach, S. Park, “Small convolution kernels for high-fidelity image restoration,” IEEE Trans. Signal Process. 39, 2263–2274 (1991).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Phys. A

R. Caprari, “Non-parametric Wiener filter for reducing noise on reproducible pure signals,” J. Phys. A 32, 3075–3094 (1999).
[CrossRef]

Opt. Eng.

J. Goodman, “A random walk through the field of speckle,” Opt. Eng. 86, 610–612 (1986).

Opt. Lett.

Other

N. Stacy, M. Burgess, M. Muller, R. Smith, “Ingara: an integrated airborne imaging radar system,” in Proceedings of the International Geoscience and Remote Sensing Symposium (Institute of Electrical and Electronics Engineers, New York, 1996), Vol. 3, pp. 1618–1620.

C. Oliver, S. Quegan, Understanding Synthetic Aperture Radar Images (Artech House, Boston, 1998).

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Figures (4)

Fig. 1
Fig. 1

Component looks of a SAR image, their sum, and their difference.

Fig. 2
Fig. 2

Slightly magnified extracts from unfiltered and filtered images.

Fig. 3
Fig. 3

Intensity profiles of highly magnified extracts from unfiltered and filtered images.

Fig. 4
Fig. 4

Complete unfiltered and filtered images.

Equations (14)

Equations on this page are rendered with MathJax. Learn more.

x(1+n)s+n=s+ns+n=s+n,
nns+n
x0s+n0,  x1s+n1.
x+x1+x0=2s+n1+n0,
x-x1-x0=n1-n0.
y(i)=m=-MM fm x+i+m.
2¯12I+1i=-IIyi-si2,
n=-MMR++m-nfn=12R++m)-R--(m, m -M, M.
R++m-n12I+1i=-II x+i+m x+i+n,
R--m12I+1i=-II x-i x-i+m.
n=-MM Rxxm-nfn=Rssm=Rxxm-Rnnm, m-M, M,
R++-m=R++m, R---m=R--m, f-m=fm,
R++mf0+n=1MR++m-n+R++m+nfn=12R++m-R--m,  m0, M.
2¯min=12m=-MM R--mfm.

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