The full-waveform hyperspectral light detection and ranging (FWHSL) data have been widely used in surface topography, vegetation detection, and 3-D urban terrain modeling, capable of revealing the spatial distribution of a target and more detailed spectral information in the vertical direction. However, the echo signals of a target would significantly vary between different spectral channels due to the reflectance characteristics and the uneven energy distribution of supercontinuum laser source. Especially, band channels with weak reflectance over a long distance would affect the extraction accuracy of waveform parameters, which are essential for retrieving the spatial and spectral information of targets. This article proposes a multichannel interconnection decomposition method to improve the extraction accuracy of distance and spectral information at each pulse using hyperspectral waveform data. Two experiments were conducted to verify the performance of long-distance detection of targets using FWHSL. The first experiment detected a standard whiteboard, a green leaf, and a yellow leaf at roughly 518 m. Results demonstrated a considerable improvement in ranging precision and spectral detection using the proposed method compared with using the optimal channel with the best data quality. The second experiment simultaneously detected two adjacent targets at a distance of approximately 518 m. Results presented clear superiority of adding waveform channels in terms of discovering overlapping components and retrieving accurate waveform parameters. The success rate of extracting two targets 60 cm apart was greatly increased from 47% to 73% through the multichannel interconnection waveform decomposition (MIWD) method.

The current full-waveform data at a single wavelength can mainly retrieve the geometric attributes of targets along the light path by detecting waveform components, resulting in the lack of spectral or color attribute information. This kind of device relies on a digital camera for acquiring the color information, however, which is inevitably limited by the lighting conditions and geometric registration errors. With the development of multispectral light detection and ranging (LiDAR) or even hyperspectral LiDAR that often utilize a supercontinuum laser source covering the whole visible light band, including red, green and blue bands, the simultaneous acquisition of color and spatial information becomes possible and makes passive imaging data no longer necessary. In this study, we propose a color restoration method for a full-waveform multispectral LiDAR (FWMSL) system. Additionally, we develop a multispectral lognormal function to fit the tailing echoes measured by FWMSL further accurately. Experimental data from our FWMSL system are used to evaluate the performance of the proposed method. The relative standard deviation, correlation coefficient (R²) and color difference ( $\mathsf{\Delta }E$ ) metrics suggest that the color restoration for the full-waveform multispectral data is feasible.

When detecting respiratory rate and heart rate in an FMCW radar room, there is a lot of static clutter and white Gaussian noise generated by hardware heat loss in the environment, which makes the separation of respiratory and heartbeat signals poor. At the same time, the harmonic component of the respiratory signal in the frequency domain will affect the estimation of heart rate. To solve the above problems, a spatial blind source estimation method was proposed to accurately estimate respiratory heart rate. Firstly, the weighted principal component analysis (WPCA) algorithm was used to extract the features of the target signal from the IF signal, and then the respiratory heart rate signal was reconstructed according to the different features. Then, the multi-signal classification (MUSIC) algorithm is used to convert the respiration and heartbeat signals into the zero domain to avoid the influence of the respective harmonic components on the detection results. The experimental results showed that the accuracy of respiratory rate detection and heart rate detection was 94.51% and 97.79%, respectively. Compared with the traditional algorithm, the proposed method is stable and has higher detection accuracy.

With the rapid development of light detection and ranging (LiDAR) technology, multispectral LiDAR (MSL) can realize three-dimensional (3D) imaging of the ground object by acquiring rich spectral information. Although color restoration has been achieved on the basis of the full-waveform data of MSL, further improvement of the visual effect of color point clouds still faces many challenges. In this paper, a highlight removal method for MSL color point clouds is proposed to explore the potential of 3D visualization. First, the MSL reflection model are introduced according to radar equation and Phong model, and the restored color of the MSL point clouds is determined to comprise diffuse and specular components. Second, a data conversion method is proposed to improve the massive point cloud processing efficiency by spatial dimension reduction and data compression. Then, the visual saliency map after color denoising is used to obtain the highlight region, the unknown information of which is recovered based on the global or local color information. Finally, three representative targets are selected and evaluated by qualitative and quantitative validation, which verifies that the method can effectively recover the high-quality highlight-free point clouds of MSL.

Full-waveform hyperspectral LiDAR offers a new approach for precise forest ecological monitoring by simultaneously acquiring the three-dimensional structure and continuous spectral information of targets. However, uncertainty in the backscattering cross-section and the inseparability of the reflectance coefficient lead to systematic underestimation of multi-echo reflectance retrieved using traditional methods. This limitation significantly hinders quantitative applications. The existing multi-echo reflectance correction using neighborhood single-echo reflectance (MCNS) method provides an effective solution by establishing proportional models between similar targets, laying an important foundation for the extraction of multi-echo reflectance. However, its applicability in complex forest scenes is limited due to its dependence on specific vegetation single-echo samples. To address this, an iterative correction method based on ground reflectance baseline, namely Bare-Ground-Echo-Based Iterative Correction of Multi-Echo Reflectance for Hyperspectral LiDAR (BGE-ICMER), is proposed. Using ground single-echo reflectance as a stable baseline, a multi-target energy distribution model is constructed based on energy conservation, and backscattering cross-section proportions for each echo are iteratively solved to recover true reflectance. Validation using a high-fidelity dataset generated by the Large-Scale remote sensing data and image Simulation framework (LESS) confirmed the effectiveness of the proposed method. This dataset encompasses three typical tree species with vegetation layers ranging from two to four, incorporates micro-topographic ground surfaces and ten spectral channels from 500 to 1000 nm, thereby capturing the structural and spectral complexity of real forests. The results showed that coefficients of determination (R²) between the corrected and true reflectance exceeded 0.9560, with an RMSE below 0.0418 and MAE below 0.0360. The average relative error was reduced from 26.66% to 10.07%, representing a 62.22% improvement in accuracy. Even in the most challenging scenarios with four-layer vegetation occlusion within this dataset, no significant error accumulation occurred. These results demonstrate the robustness and effectiveness of the proposed method for multi-echo reflectance extraction. This study lays a foundation for more accurate forest biochemical attribute assessment and enables the vertical characterization of multiple targets using high-resolution spectral reflectance.

The almost sure local central limit theorem is a general result which contains the almost sure global central limit theorem. Let $\{X_{k},k\geq 1\}${Xk,k≥1} be a strictly stationary negatively associated sequence of positive random variables. Under the regular conditions, we discuss an almost sure local central limit theorem for the product of some partial sums $(\prod_{i=1}^{k} S_{k,i}/((k-1)^{k}\mu^{k}))^{\mu/(\sigma\sqrt{k})}$(∏i=1kSk,i/((k−1)kμk))μ/(σk) , where $\mathbb{E}X_{1}=\mu$EX1=μ , $\sigma^{2}={\mathbb{E}(X_{1}-\mu)^{2}}+2\sum_{k=2}^{\infty}\mathbb{E}(X_{1}-\mu)(X_{k}-\mu)$σ2=E(X1−μ)2+2∑k=2∞E(X1−μ)(Xk−μ) , $S_{k,i}=\sum_{j=1}^{k}X_{j}-X_{i}$Sk,i=∑j=1kXj−Xi .