Abstract: In order to improve the quality of 3D point cloud, a low-rank collaborative estimation method based on L₁ sparse optimization is proposed. Method can both restore sharp features and denoise. Firstly, robust principal component analysis is used for low-rank modeling and estimation to avoid the influence of outliers, and the model is adjusted according to the change of normal field to realize anisotropic adaptive denoising in local area. Secondly, in order to improve the efficiency, the local curvature of each point is estimated to recognize sharp feature. Iterative thresholding method and inexact augmented Lagrange multiplier method are combined to solve the low-rank model in different regions of point cloud. Thirdly, the point positions are determined by collaborative estimation from local result to achieve global reconstruction of 3D point cloud. Finally, the sharp edge features are restored by projection optimization of feature points to solve the problems of sharp feature degradation and irregular edges. Experimental results based on public dataset show that the proposed algorithm has achieved improvements in terms of subjective visual effects, as well as reconstruction accuracy and efficiency. Compared with MRPCA algorithm, the accuracy and efficiency are improved by 10.22% and 56.52% respectively. It can effectively filter noise and restore sharp features while the original feature information of point cloud is retained, and the reconstruction effect is superior.