Objective For some complex urban scenes under laser echo, the corresponding full-waveform echo data is inevitably mixed with various noises, which affects the extraction of effective signals. Traditional Gaussian noise reduction algorithms struggle to meet the filtering requirements of both effective and noise signals. In recent years, there has been a greater focus on the filtering effect of wavelet noise reduction, which is affected by several parameters. Therefore, in this paper, a parameter optimization wavelet noise reduction algorithm is proposed to improve the filtering effect of full-waveform data.

Methods The parameter selection of wavelet denoising is the central issue of this research. This paper employs one-dimensional wavelet denoising function (WDEN) in MATLAB to select the threshold selection criterion (TPTR), threshold usage method (SORH), threshold processing with noise change parameter (SCAL), decomposition layer (NBD), and wavelet basis function name (WNAME) five control parameters for filtering, calculates the filtering results under each parameter combination, and compares to obtain the wavelet optimal combination of control parameters. The specific steps of the parameter optimization wavelet denoising algorithm and its verification process are as follows:

1) Set five input parameter types (TPTR, SORH, SCAL, NBD, WNAME) according to the waveform characteristics, and reconstruct the echo waveform by referring to the wavelet formula (Eqs. 1~7) and the one-dimensional noise reduction function.

2) Taking the maximization of signal-to-noise ratio as the optimization goal, extract the corresponding best parameter combination of each verification waveform.

3) In the final verification, analyze the obtained experimental results according to the evaluation index of noise reduction effect.

Results and Discussions Table 3 is the optimal control parameter combination of ten waveforms, which is determined according to the maximum signal-to-noise ratio in each waveform parameter combination. The trend of these parameters is clearly visible in this table, which shows that, with the exception of the wavelet basis, the other four parameters outside the function are exactly the same. Table 4 compares the filtering effects of Gaussian, block Gaussian, and wavelet filtering under different indicators. The filtering effect in descending order is that of wavelet filtering, Gaussian filtering and block Gaussian filtering. Specific to each indicator of each waveform, wavelet filtering is far superior to the other two methods. The signal-to-noise ratio and peak signal-to-noise ratio of wavelet filtering are generally higher than the other two methods by 25 dB--35 dB, and its root mean square error and average absolute error are an order of magnitude lower. In the second-to-last row of Table 5, the average value of the ten verification waveforms is 35.84 m. The average values of the even-odd inflection point Gaussian decomposition method and the GLAH14 data file algorithm are 9.92 m and 16.42 m, respectively. They are not particularly accurate in comparison. The effective inflection point of the weak signal cannot be identified in the implementation of the even-odd inflection point Gaussian decomposition method in the urban feature scene, as shown in Fig. 7. If you want to be more precise, you must consider other methods based on the problems listed above. This article presents a component information correction method based on this, that is, a method of correcting the center position information based on the extracted Gaussian component information. The average elevation using this method is 35.47 m, which is very close to the measured average elevation of 35.84 m, and the root mean square error is only 1.02, which meets the requirements for accurate measurement of ground features, as shown in the last two columns of Table 5. The height measurement results of only the wavelet filtering under parameter optimization and the other operation unchanged methods are shown in the 5th, 7th, and 9th columns of the table. The average value of the height measurement results of the inflection point decomposition method is therefore increased from 9.92 m to 14.37 m, the root mean square error has also been reduced from 42.07 to 29.00, and the effective peak decomposition algorithm and correction algorithm therefore have limited improvements.

Conclusions In summary, the wavelet noise reduction algorithm under parameter optimization can extract the appropriate combination of many control parameters, and achieve an extremely excellent filtering effect compared to the traditional method. Data with better filtering effects can improve measurement results under less accurate methods in subsequent verification, but help for more accurate measurement methods is limited. Wavelet filtering has an effect on full-waveform data height measurement. It has a positive effect, but the focus of height measurement research should be on improving the decomposition method and adjusting the threshold control parameters in the algorithm.