A noise reduction method for portable Lidar Echo data using statistical technique
2 Processing algorithm of the NORMALS
In the case where we apply the CCA to noise reduction of lidar echo data, the method for assignment of characteristic variates is important. Here we denote lidar echo signal which is acquired in normal operation by S1, and assume that S1, can be described as:
S
1 = S + N
1
Where S: backscatter signal from scattere,
N
1: noise component.
Since it is difficult to estimate N
1, subtraction operation cannot be applied to noise reduction. Then we use lidar echo single which is acquired in non-lasing operation in place of N1, and denote this non-lasing signal by S2. The S2 can be described as:
S
2=N
2
Where N
2: noise component.
In the case where S
1 and S
2 are assigned to the characteristic variates of GROUP-1, the
Necessary conditions for the assignment of two characteristic variates of GOUPS-2 can be described as follows.
- the outline wave form data of S is required as the characteristic variate S1' of GROUND-2
- The outline wave form data of N1 is required as the characteristic variate S2' of GROUP-2
In the NORMALS, moving averaged S1data S2 data is assigned of S1, and S2, respectively. The schematic processing flow of the NORMALS is shown in Fig.
Fig. 2. Flow of processing
3. Experimant and Discussion
1 Simulation
Fig. 3 shows an artificial backscatter datum S (made from probability density function of X2 distribution with six degree of freedom) for the simulation. Fig. 4 (a) and (b) show the results by the NORMALS and by the moving average method (the same data as S1). From these results, we see that the noise component is reduced almost completely by the NORMALS.
Fig. 4. An artificial A-scope datum(p.d.f of X2 distrubution, deg. of freedom = 6)
Fig. 5. Simulation results
2 Actual Lidar Echo Data
Fig. 6 (a) and (b) show actual lidar echo data with lasing (S1) and without lasing (S2), respectively. We used the portable YAG [3], [4] lidar system that we have developed for data acquisition. Fig. 7 (a) and (b) show the results by the NORMALS and by the moving average method (the same data as S1). From these results, while the moving average method distorts both the noise component and the wave form of the backscatter signal, the NROMALS only reduces the noise component without distorting the backscatter signal. As the result of measurements, amplitude of noise component and mean square error against ground level were reduced by the NORMALS 35% AND 62%, respectively.
Summary
The validity of the proposed method, the NORMALS, was confirmed through comparison of the result by moving average method from the view point of the performance of noise reduction and the wave form distortion. As the results of experiments, the NORMALS has the advantage of an effective noise reduction without wave form distortion of backscatter signal. Improvement of the performance is a subject for a future study.
Acknowledgements:
The authors are grateful to Dr. Koji Kajiwara, Institute of Industrial Science. University of Tokyo. JAPAN, and Mr. Kithsiri Perera, Remote Sensing & Image Research Centre. Chiba University, JAPAN, for their helpful advices and supports.
References
- Rao, C.R. Linear Statistical Inference and Its Applications (2nd edition), John Wiley & Sons (1973)
- Morrison, D.F.: Multivariate Statistical Methods (3rd edition,) McGraw-Hill (1990)
- Takeuchi, N., et al. A Portable Lidar Using Diode-Pumped YAG Laser, Proc, of 16th International Laser Radar Conference, 695/698 (1992)
- Okumura, H. et al.: A High Speed Singal Processing System for a Diode-Pmped YAG Lidar, Proc. Of 16th International Laser Radar Co
Fig. 6. Actual lidar data
Fig. 7. Processing results.
