Abstract

We propose a new, to our knowledge, denoising method for lidar signals based on a regression model and a wavelet neural network (WNN) that permits the regression model not only to have a good wavelet approximation property but also to make a neural network that has a self-learning and adaptive capability for increasing the quality of lidar signals. Specifically, we investigate the performance of the WNN for antinoise approximation of lidar signals by simultaneously addressing simulated and real lidar signals. To clarify the antinoise approximation capability of the WNN for lidar signals, we calculate the atmosphere temperature profile with the real signal processed by the WNN. To show the contrast, we also demonstrate the results of the Monte Carlo moving average method and the finite impulse response filter. Finally, the experimental results show that our proposed approach is significantly superior to the traditional methods.

© 2005 Optical Society of America

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References

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  1. P. S. Argall, R. J. Sica, LIDAR in the Encyclopedia of Atmospheric Sciences (Academic, London, 2002).
  2. S. Lerkvarnyu, “Moving average method for time series lidar data,” http://www.gisdevelopment.net/aars/acrs/1998/ps3/ps3016.shtml .
  3. S. Amoruso, A. Amodeo, M. Armenante, A. Boselli, “Development of a tunable IR lidar system,” Opt. Lasers Eng. 37, 521–532 (2002).
    [CrossRef]
  4. K. Stelmaszczyk, “New method of elaboration of the lidar signal,” Appl. Phys. B 70, 295–299 (2000).
    [CrossRef]
  5. C. Andrien, “Robust full Bayesian learning for radial basis networks,” Neural Comput. 13, 2359–2407 (2001).
    [CrossRef]
  6. A. B. Utkin, “Detection of small forest fires by lidar,” Appl. Phys. B 74, 77–83 (2002).
    [CrossRef]
  7. V. Kreinovich, “Wavelet neural network are asymptotically optimal approximators for function of one variable,” in IEEE World Congress on Computational Intelligence, 1994 IEEE International Conference (IEEE, Piscataway, N.J., 1994), Vol. 1, pp. 299–304.
  8. D. S. Huang, Systematic Theory of Neural Networks for Pattern Recognition (Publishing House of Electronic Industry of China, Beijing, 1996).
  9. F. G. Fernald, “Analysis of atmospheric lidar observations: some comments,” Appl. Opt. 23, 652–653 (1984).
    [CrossRef] [PubMed]
  10. D. S. Huang, Y. Q. Han, “A detection method of high resolution radar targets based on position correlation,” J. Electron. 5, 107–115 (1998).
  11. C. F. Bas, “The layered perceptron versus the Neyman–Pearson optimal detection,” in Proceedings of the International Joint Conference on Neural Networks (IEEE, Piscataway, N.J., 1992), pp. 1486–1489.
  12. D. S. Huang, Z. Bao, “The study of recognition technique of radar targets one dimensional images based on radial basis function network,” J. Electron. 12, 200–210 (1995).
  13. D. S. Huang, Intelligent Signal Processing Technique for High Resolution Radars (Publishing House of Machine Industry of China, Beijing, 2001).
  14. I. Daubechise, “The wavelet transform, time-frequency localization and signal analysis,” IEEE Trans. Inf. Theory 36, 961–1005 (1990).
    [CrossRef]
  15. J. Zhang, “Wavelet neural networks for function learning,” IEEE Trans. Signal Process. 43, 1485–1497 (1995).
    [CrossRef]
  16. L. Cao, Y. Hong, “Predicting chaotic time series with wavelet networks,” Physica D 85, 225–238 (1995).
    [CrossRef]
  17. See http://www.atmosphere.mpg.de/enid/791 .
  18. A. Hauchecorne, M. L. Chanin, “Density and temperature profiles obtained by lidar between 35 and 75 km,” Geophys. Res. Lett. 7, 565–568 (1980).
    [CrossRef]
  19. T. Shibata, M. Kobuchi, M. Maeda, “Measurements of density and temperature profiles in the middle atmosphere with XeF lidar,” Appl. Opt. 25, 685–688 (1986).
    [CrossRef] [PubMed]

2002 (2)

S. Amoruso, A. Amodeo, M. Armenante, A. Boselli, “Development of a tunable IR lidar system,” Opt. Lasers Eng. 37, 521–532 (2002).
[CrossRef]

A. B. Utkin, “Detection of small forest fires by lidar,” Appl. Phys. B 74, 77–83 (2002).
[CrossRef]

2001 (1)

C. Andrien, “Robust full Bayesian learning for radial basis networks,” Neural Comput. 13, 2359–2407 (2001).
[CrossRef]

2000 (1)

K. Stelmaszczyk, “New method of elaboration of the lidar signal,” Appl. Phys. B 70, 295–299 (2000).
[CrossRef]

1998 (1)

D. S. Huang, Y. Q. Han, “A detection method of high resolution radar targets based on position correlation,” J. Electron. 5, 107–115 (1998).

1995 (3)

D. S. Huang, Z. Bao, “The study of recognition technique of radar targets one dimensional images based on radial basis function network,” J. Electron. 12, 200–210 (1995).

J. Zhang, “Wavelet neural networks for function learning,” IEEE Trans. Signal Process. 43, 1485–1497 (1995).
[CrossRef]

L. Cao, Y. Hong, “Predicting chaotic time series with wavelet networks,” Physica D 85, 225–238 (1995).
[CrossRef]

1990 (1)

I. Daubechise, “The wavelet transform, time-frequency localization and signal analysis,” IEEE Trans. Inf. Theory 36, 961–1005 (1990).
[CrossRef]

1986 (1)

1984 (1)

1980 (1)

A. Hauchecorne, M. L. Chanin, “Density and temperature profiles obtained by lidar between 35 and 75 km,” Geophys. Res. Lett. 7, 565–568 (1980).
[CrossRef]

Amodeo, A.

S. Amoruso, A. Amodeo, M. Armenante, A. Boselli, “Development of a tunable IR lidar system,” Opt. Lasers Eng. 37, 521–532 (2002).
[CrossRef]

Amoruso, S.

S. Amoruso, A. Amodeo, M. Armenante, A. Boselli, “Development of a tunable IR lidar system,” Opt. Lasers Eng. 37, 521–532 (2002).
[CrossRef]

Andrien, C.

C. Andrien, “Robust full Bayesian learning for radial basis networks,” Neural Comput. 13, 2359–2407 (2001).
[CrossRef]

Argall, P. S.

P. S. Argall, R. J. Sica, LIDAR in the Encyclopedia of Atmospheric Sciences (Academic, London, 2002).

Armenante, M.

S. Amoruso, A. Amodeo, M. Armenante, A. Boselli, “Development of a tunable IR lidar system,” Opt. Lasers Eng. 37, 521–532 (2002).
[CrossRef]

Bao, Z.

D. S. Huang, Z. Bao, “The study of recognition technique of radar targets one dimensional images based on radial basis function network,” J. Electron. 12, 200–210 (1995).

Bas, C. F.

C. F. Bas, “The layered perceptron versus the Neyman–Pearson optimal detection,” in Proceedings of the International Joint Conference on Neural Networks (IEEE, Piscataway, N.J., 1992), pp. 1486–1489.

Boselli, A.

S. Amoruso, A. Amodeo, M. Armenante, A. Boselli, “Development of a tunable IR lidar system,” Opt. Lasers Eng. 37, 521–532 (2002).
[CrossRef]

Cao, L.

L. Cao, Y. Hong, “Predicting chaotic time series with wavelet networks,” Physica D 85, 225–238 (1995).
[CrossRef]

Chanin, M. L.

A. Hauchecorne, M. L. Chanin, “Density and temperature profiles obtained by lidar between 35 and 75 km,” Geophys. Res. Lett. 7, 565–568 (1980).
[CrossRef]

Daubechise, I.

I. Daubechise, “The wavelet transform, time-frequency localization and signal analysis,” IEEE Trans. Inf. Theory 36, 961–1005 (1990).
[CrossRef]

Fernald, F. G.

Han, Y. Q.

D. S. Huang, Y. Q. Han, “A detection method of high resolution radar targets based on position correlation,” J. Electron. 5, 107–115 (1998).

Hauchecorne, A.

A. Hauchecorne, M. L. Chanin, “Density and temperature profiles obtained by lidar between 35 and 75 km,” Geophys. Res. Lett. 7, 565–568 (1980).
[CrossRef]

Hong, Y.

L. Cao, Y. Hong, “Predicting chaotic time series with wavelet networks,” Physica D 85, 225–238 (1995).
[CrossRef]

Huang, D. S.

D. S. Huang, Y. Q. Han, “A detection method of high resolution radar targets based on position correlation,” J. Electron. 5, 107–115 (1998).

D. S. Huang, Z. Bao, “The study of recognition technique of radar targets one dimensional images based on radial basis function network,” J. Electron. 12, 200–210 (1995).

D. S. Huang, Systematic Theory of Neural Networks for Pattern Recognition (Publishing House of Electronic Industry of China, Beijing, 1996).

D. S. Huang, Intelligent Signal Processing Technique for High Resolution Radars (Publishing House of Machine Industry of China, Beijing, 2001).

Kobuchi, M.

Kreinovich, V.

V. Kreinovich, “Wavelet neural network are asymptotically optimal approximators for function of one variable,” in IEEE World Congress on Computational Intelligence, 1994 IEEE International Conference (IEEE, Piscataway, N.J., 1994), Vol. 1, pp. 299–304.

Lerkvarnyu, S.

S. Lerkvarnyu, “Moving average method for time series lidar data,” http://www.gisdevelopment.net/aars/acrs/1998/ps3/ps3016.shtml .

Maeda, M.

Shibata, T.

Sica, R. J.

P. S. Argall, R. J. Sica, LIDAR in the Encyclopedia of Atmospheric Sciences (Academic, London, 2002).

Stelmaszczyk, K.

K. Stelmaszczyk, “New method of elaboration of the lidar signal,” Appl. Phys. B 70, 295–299 (2000).
[CrossRef]

Utkin, A. B.

A. B. Utkin, “Detection of small forest fires by lidar,” Appl. Phys. B 74, 77–83 (2002).
[CrossRef]

Zhang, J.

J. Zhang, “Wavelet neural networks for function learning,” IEEE Trans. Signal Process. 43, 1485–1497 (1995).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. B (2)

A. B. Utkin, “Detection of small forest fires by lidar,” Appl. Phys. B 74, 77–83 (2002).
[CrossRef]

K. Stelmaszczyk, “New method of elaboration of the lidar signal,” Appl. Phys. B 70, 295–299 (2000).
[CrossRef]

Geophys. Res. Lett. (1)

A. Hauchecorne, M. L. Chanin, “Density and temperature profiles obtained by lidar between 35 and 75 km,” Geophys. Res. Lett. 7, 565–568 (1980).
[CrossRef]

IEEE Trans. Inf. Theory (1)

I. Daubechise, “The wavelet transform, time-frequency localization and signal analysis,” IEEE Trans. Inf. Theory 36, 961–1005 (1990).
[CrossRef]

IEEE Trans. Signal Process. (1)

J. Zhang, “Wavelet neural networks for function learning,” IEEE Trans. Signal Process. 43, 1485–1497 (1995).
[CrossRef]

J. Electron. (2)

D. S. Huang, Z. Bao, “The study of recognition technique of radar targets one dimensional images based on radial basis function network,” J. Electron. 12, 200–210 (1995).

D. S. Huang, Y. Q. Han, “A detection method of high resolution radar targets based on position correlation,” J. Electron. 5, 107–115 (1998).

Neural Comput. (1)

C. Andrien, “Robust full Bayesian learning for radial basis networks,” Neural Comput. 13, 2359–2407 (2001).
[CrossRef]

Opt. Lasers Eng. (1)

S. Amoruso, A. Amodeo, M. Armenante, A. Boselli, “Development of a tunable IR lidar system,” Opt. Lasers Eng. 37, 521–532 (2002).
[CrossRef]

Physica D (1)

L. Cao, Y. Hong, “Predicting chaotic time series with wavelet networks,” Physica D 85, 225–238 (1995).
[CrossRef]

Other (7)

See http://www.atmosphere.mpg.de/enid/791 .

D. S. Huang, Intelligent Signal Processing Technique for High Resolution Radars (Publishing House of Machine Industry of China, Beijing, 2001).

P. S. Argall, R. J. Sica, LIDAR in the Encyclopedia of Atmospheric Sciences (Academic, London, 2002).

S. Lerkvarnyu, “Moving average method for time series lidar data,” http://www.gisdevelopment.net/aars/acrs/1998/ps3/ps3016.shtml .

C. F. Bas, “The layered perceptron versus the Neyman–Pearson optimal detection,” in Proceedings of the International Joint Conference on Neural Networks (IEEE, Piscataway, N.J., 1992), pp. 1486–1489.

V. Kreinovich, “Wavelet neural network are asymptotically optimal approximators for function of one variable,” in IEEE World Congress on Computational Intelligence, 1994 IEEE International Conference (IEEE, Piscataway, N.J., 1994), Vol. 1, pp. 299–304.

D. S. Huang, Systematic Theory of Neural Networks for Pattern Recognition (Publishing House of Electronic Industry of China, Beijing, 1996).

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Figures (10)

Fig. 1
Fig. 1

Schematic diagram of a genetic lidar system.

Fig. 2
Fig. 2

Simulated lidar signal without noise.

Fig. 3
Fig. 3

Real lidar signal with noise.

Fig. 4
Fig. 4

Block diagram of the WNN.

Fig. 5
Fig. 5

Power spectral density of colored noises.

Fig. 6
Fig. 6

Contaminated signal.

Fig. 7
Fig. 7

Antinoise approximation result of the simulated signal.

Fig. 8
Fig. 8

Antinoise approximation result of the real signal.

Fig. 9
Fig. 9

Atmosphere temperature’s principle profile in theory.

Fig. 10
Fig. 10

Atmosphere temperature profiles calculated by the real lidar signal.

Equations (12)

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p r ( λ L ) = C R 2 h 2 O ( R ) β ( λ L , R ) 4 π × exp [ - 2 0 R k e ( λ L , R ) d R ] ,
W f = a 1 / 2 - f ( x ) ψ ( x - b a ) d x = f ( x ) , ψ a , b ( x ) ,
W f i j = 2 i / 2 f ( x ) ψ ( 2 i x - j ) d x = f ( x ) , ψ i j ( x ) ,
f ( x ) = i j θ i j ψ i j ( x ) ,
f ^ ( x , θ ) = i = M 1 M m j = N 1 N n θ i j ψ i j ( x ) = θ T W ( x ) ,             M m N n Z ,
θ = [ θ M 1 , N 1 , , θ M 1 , N n , , θ M m , N 1 , , θ M m , N n ] T , W ( x ) = [ ψ M 1 , N 1 ( x ) , , ψ M 1 , N n ( x ) , , ψ M m , N 1 ( x ) , , ψ M m , N n ( x ) ] T .
f ^ ( x , θ ) = i = M 1 M m j = N 1 N n θ i j ψ i j ( c T x ) = θ T W ( c T x ) ,             M m N n Z .
f ( x ) - f ^ ( x , θ ) 2 .
y = f ( x ) + ,
n 2 ( t ) = - 1.5 n 2 ( t - 1 ) - 0.75 n 2 ( t - 2 ) - 0.125 n 2 ( t - 3 ) + n 1 ( t ) + 0.5 ,
SNR = 10 log [ ( i = 1 n I k 2 ) / i = 1 n ( I k - I ^ k ) 2 ] ,
N ( z ) = C [ n ( z ) / z 2 ] ,

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