Fig. 1. Flow chart of the proposed method
Fig. 2. Sketch map of extracting the peak positions and numbers of the target response waveform (TRW) based on the boosted RL deconvolution method
Fig. 3. Location of the study site and data trajectories of the GEDI and airborne lidar
Fig. 4. Prescribed parameter distributions of the known-parameter TRW and an example of the TRW
Fig. 5. Decomposed results of the received waveform by the DRET and DGDL methods
Fig. 6. The processed results of the known-parameter waveform data set obtained by the DRET and DGDL methods
Fig. 7. Extracted errors of the waveform parameters and the successful detection rates of the component numbers by the DRET and DGDL methods
Fig. 8. Decomposition results of airborne simulation data by the DRET and DGDL methods
Fig. 9. Decomposition results of the GEDI data by the DRET and DGDL methods
Fig. 10. Point cloud distributions of the vegetated target
Fig. 11. Distributions of the canopy height errors under different tree heights
Source | Amplitude/V | Peak position/ns | Pulse width/ns | System response | 1 | 20 | 15.6 | Target response | 0.2-1 | 300-400 | 5-15 |
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Table 1. Parameter setting of known-parameter waveform data set
Method | Component | I | u | b | a | Evaluation criterion | $ {C}_{x} $![]() ![]() | $ {\delta }_{x} $![]() ![]() | $ {\tau }_{I} $![]() ![]() | $ {\tau }_{u} $![]() ![]() | $ {\tau }_{b} $![]() ![]() | 1此处NA表示DGDL方法中不存在偏度系数。
| 2此处NA表示该分量为错误分量,无法计算对应的参数误差。
| DRET | 1 | 0.69 | 345.05 | 7.58 | 0.01 | 0.99 | 1.37 | 1.42% | 0.05% | 3.69% | 2 | 0.51 | 366.26 | 10.43 | 0.05 | 2.00% | 0.74% | 2.52% | DGDL | 1 | 0.61 | 343.89 | 7.16 | NA 1 | 0.97 | 2.63 | 12.86% | 2.11% | 8.34% | 2 | 0.22 | 361.21 | 15.02 | NA 1 | NA 2 | NA 2 | NA 2 | 3 | 0.31 | 368.55 | 10.98 | NA 1 | 18.97% | 2.31% | 6.22% |
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Table 2. Detailed waveform parameters and evaluation indicators of the results extracted by the two methods
Evaluation index | DRET | DGDL | $ {C}_{x} $ | 0.987 | 0.966 | $ {\delta }_{x} $ | 1.217 | 2.305 | $ {\tau }_{I} $ | 2.18% | 7.56% | $ {\tau }_{u} $ | 0.52% | 3.69% | $ {\tau }_{b} $ | 2.33% | 6.47% | $ {r}_{s} $ | 98.70% | 64.25% |
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Table 3. Average value of the evaluation indexes of the two methods
Evaluation index | DRET | DGDL | $ {C}_{x} $ | Max | 0.999 | 0.991 | Min | 0.937 | 0.872 | Average | 0.995 | 0.986 | Standard deviation | 0.012 | 0.034 | $ {\delta }_{x} $ | Max | 9.326 | 14.273 | Min | 0.607 | 1.988 | Average | 1.869 | 3.516 | Standard deviation | 1.291 | 2.936 |
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Table 4. Correlation coefficient (
\begin{document}$C_x $\end{document}![]()
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) and RMSE (
\begin{document}$\delta_x $\end{document}![]()
![]()
) of the DRET and the DGDL methods for the processing results of the airborne simulation data
Evaluation index | DRET | DGDL | $ {C}_{x} $ | Max | 0.999 | 0.982 | Min | 0.939 | 0.854 | Average | 0.993 | 0.977 | Standard deviation | 0.037 | 0.062 | $ {\delta }_{x} $ | Max | 9.412 | 15.504 | Min | 0.449 | 3.075 | Average | 1.953 | 4.248 | Standard deviation | 1.363 | 3.712 |
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Table 5. Correlation coefficient (
\begin{document}$C_x $\end{document}![]()
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) and RMSE (
\begin{document}$\delta_x $\end{document}![]()
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) of the DRET and the DGDL methods for the processing results of the GEDI data