3D Terrain Reconstruction Of LiDAR Sparse Point Cloud Based On Compressed Sensing Theory

Due to the ability of airborne LiDAR to penetrate vegetation and obtain accurate ground points,it has become the primary sensor for directly acquiring three-dimensional coordinates of the ground.High-precision three-dimensional terrain has become one of the most important applications in the past twenty years.However,in areas with dense vegetation cover,the ground points obtained by airborne LiDAR are also sparse,unevenly distributed,and even have some gaps,and various traditional algorithms cannot extract terrain information.In this paper,in response to the current situation of sparse distribution of airborne LiDAR point clouds in densely vegetated areas leading to DEM reconstruction that cannot meet the requirements of high-precision mapping,the terrain is viewed as an elevation signal,and compressive sensing theory is introduced to achieve LiDAR point cloud data reconstruction.A three-dimensional topographic reconstruction method of sparse point cloud based on compressed sensing theory is proposed.The main research contents are as follows:1.The advantages and disadvantages of the existing algorithms for filtering and interpolation in the point cloud data processing process in the face of point cloud data in complex scenarios are studied.Focus on discussing the problems existing in mainstream filtering algorithms in complex scenes with dense vegetation and propose an adaptive triangulation filtering guided by slope for airborne LiDAR point cloud data to provide more accurate ground point data for subsequent compressive sensing terrain reconstruction work.2.Innovatively introduce the compressive sensing theorem into the application of laser radar and process the ground surface from the perspective of "signal".Train an overcomplete dictionary set with a large amount of terrain training data,study the sparse point cloud reconstruction based on the overcomplete dictionary set,use the terrain feature correlation matrix to match the sparse point cloud data with sample data,select the sample data with the highest matching degree in the dictionary set for overcomplete dictionary to reconstruct the terrain.Use two datasets containing various terrain features for experiments,analyze the influence of point cloud data sampling rate scale on the reconstruction effect under different terrain conditions,and quantitatively evaluate the effectiveness of the algorithm in this study through peak signal-to-noise ratio（PSNR）、maximum error(E_max)、average error(E_avg)and root-mean-square error（RMSE）.3.In response to the problem of clustering of the point cloud signal reconstructed by compressive sensing when the sampling rate is too low,introduce a three-dimensional surface reconstruction algorithm with strong defect repair capability,the Poisson equation,to predict and repair the terrain holes to obtain a more realistic three-dimensional terrain and compensate for the deficiency of compressive sensing algorithm in terrain reconstruction of laser radar point cloud holes.The research results show that the filtering algorithm proposed in this paper can achieve good filtering effects in complex scenes with dense vegetation.Recovering sparse LiDAR point clouds and three-dimensional terrain reconstruction from the perspective of signal processing is feasible.Compressive sensing theory can be successfully applied to the three-dimensional terrain reconstruction of sparse point clouds,and the Poisson reconstruction can effectively compensate for terrain holes,thereby improving the difficult situation of obtaining highprecision DEMs in mountainous areas with high vegetation coverage.