A Method for Solving LiDAR Waveform Decomposition Parameters Based on a Variable Projection Algorithm

Light detection and ranging (LiDAR) is commonly used to create high-resolution maps; however, the efficiency and convergence of parameter estimation are difficult. To address this issue, we evaluated the structural characteristics of received LiDAR signals by decomposing them into Gaussian functions and applied the variable projection algorithm of the separable nonlinear least-squares problem to the process of waveform fitting. First, using a variable projection algorithm, we separated the linear (amplitude) and nonlinear (center position and width) parameters in the Gaussian function model; the linear parameters are expressed with nonlinear parameters by the function. Thereafter, the optimal estimation of the characteristic parameters of the Gaussian function components was transformed into a least-squares problem only comprising nonlinear parameters. Finally, the Levenberg–Marquardt algorithm was used to solve these nonlinear parameters, whereas the linear parameters were calculated simultaneously in each iteration, and the estimation results satisfying the nonlinear least-square criterion were obtained. Five groups of waveform decomposition simulation data and ICESat/GLAS satellite LiDAR waveform data were used for the parameter estimation experiments. During the experiments, for the same accuracy, the separable nonlinear least-squares optimization method required fewer iterations and lesser calculation time than the traditional method of not separating parameters; the maximum number of iterations was reached before the traditional method converged to the optimal estimate. The method of separating variables only required 14 iterations to obtain the optimal estimate, reducing the computational time from 1128 s to 130 s. Therefore, the application of the separable nonlinear least-squares problem can improve the calculation efficiency and convergence speed of the parameter solution process. It can also provide a new method for parameter estimation in the Gaussian model for LiDAR waveform decomposition.

EXPLORING THE POTENTIAL OF FULL WAVEFORM AIRBORNE LIDAR FEATURES AND ITS FUSION WITH RGB IMAGE IN CLASSIFICATION OF A SPARSELY FORESTED AREA

Precise measurements of forest trees is very important in environmental protection. Measuring trees parameters by use of ground- based inventories is time and cost consuming. Employing advanced remote sensing techniques to obtain forest parameters has recently made a great progress step in this research area. Among the information resources of the study field, full waveform LiDAR data have attracted the attention of researchers in the recent years. However, decomposing LiDAR waveforms is one of the challenges in the data processing. In fact, the procedure of waveform decomposition causes some of the useful information in waveforms to be lost. In this study, we aim to investigate the potential use of non-decomposed full waveform LiDAR features and its fusion with optical images in classification of a sparsely forested area. We consider three classes including i) ground, ii) Quercus wislizeni and iii) Quercus douglusii for the classification procedure. In order to compare the results, five different strategies, namely i) RGB image, ii) common LiDAR features, iii) fusion of RGB image and common LiDAR features, iv) LiDAR waveform structural features and v) fusion of RGB image and LiDAR waveform structural features have been utilized for classifying the study area. The results of our study show that classification via using fusion of LiDAR waveform features and RGB image leads to the highest classification accuracy.

Retrieval of Nearshore Bathymetry around Ganquan Island from LiDAR Waveform and QuickBird Image

Optical remote sensing is an effective means of water depth measurement, but the current approach of mainstream bathymetric retrieval requires a large amount of onsite measurement data. Such data are hard to obtain from places where underwater terrains are complicated and unsteady, and from sea areas affected by issues with rights and conflicts of interest. In recent years, the emergence of airborne light detection and ranging (LiDAR) provided a new technical means for field bathymetric survey. In this study, water depth inversion was carried out around an island far from the mainland by using remote sensing images and real LiDAR waveform data. Multi-Gaussian function fitting was proposed to extract water depth data from waveform data, and bathymetric values were used as control and validation data of the active and passive combination of water depth inversion. Results show that the relative error was 5.6% for the bathymetric retrieval from LiDAR waveform data, and the accuracy meets the requirements of ocean bathymetry. The average relative error of water depth inversion based on active and passive remote sensing was less than 9%. The method used in this study can also reduce the use of LiDAR data and the cost, thus providing a new idea for future coastal engineering application and construction.