Spaceborne full-waveform lidar, as an advanced remote sensing technology, has been widely applied in various fields due to its ability to record detailed terrain and vegetation information. However, the data from spaceborne full-waveform lidar can be affected by factors such as dark current, photodetector performance, the surrounding environment of the target being detected, and background light during the acquisition process. These factors introduce significant noise into the original waveform signals, interfering with the extraction of effective echo information for target inversion analysis. To address the common problem of waveform amplitude reduction in existing classical filtering algorithms, this paper proposes an adaptive filtering compensation method for waveform amplitude. By utilizing the bat algorithm to optimize Gaussian sharpening operator parameters and convolving the Gaussian sharpening operator with the filtered waveform data, waveform compensation is achieved through adaptive iteration to ensure optimal compensation effects. This paper conducts experimental verification on GEDI (Global Ecosystem Dynamics Investigation) echo data, comparing the proposed method with various filtering algorithms. After filtering, the highest peak amplitude was reduced by an average of 9.0077, while the difference between the highest peaks of the waveform after Gaussian sharpening compensation and the original waveform was only 0.0182 on average. Moreover, the average signal-to-noise ratio improved from 30.0235dB to 33.2609dB, representing a relative increase of 10.78%. The results indicate that this method, in conjunction with filtering methods, can remove noise while retaining more of the original waveform feature information. This provides more accurate data for further extraction of waveform information for geophysical parameter inversion and target classification and is applicable to a variety of filtering methods.