Research And Application Of Approximate Decomposition Completion Algorithm Based On Sparse Optimization

The completion problem is very important in machine vision and signal processing.The matrix completion algorithm takes advantage of the structural property of the image and introduces low-rank prior knowledge to predict and fill missing elements,which has a high explanatory ability for image restoration.The matrix completion algorithm ignores the correlation between channels due to the way of processing each channel superposition.When processing higher-order data,the calculation cost increases significantly with the increase in data size.Tensor ccompletion algorithm can make full use of the correlation between channels,improve the recovery precision and speed,and thus become one of the research hotspots of completion problems.Truncated nuclear norm,as a good convex substitute for rank function,is used as a low-rank representation.TNN-SR algorithm combined with sparse prior knowledge has higher recovery accuracy,but its calculation cost is higher.A new matrix completion algorithm named LNM-QR based on QR decomposition and l_2,1norm minimization is pro-posed to solve the singular value of the matrix by approximate decomposition.Inspired by this,this thesis proposes a matrix completion algorithm LNM-SR based on l_2,1norm min-imization problem and sparse regularization and further adds weights to the algorithm.A l_2,1norm minimization and sparse regularization matrix completion algorithm IRLNM-SR based on iterative reweighting is proposed,which has higher recovery accuracy in block occlusion restoration experiments.Experiments show that the algorithms LNM-SR and IRLNM-SR have high recovery accuracy and fast computation speed.Although the tensor completion algorithm SRTD combined with low-rank priors and sparse priors has higher recovery accuracy,it still has disadvantages in computing speed.Based on the SRTD algorithm,a truncated nuclear norm based on tensor QR decomposi-tion and a sparse regularization tensor completion algorithm（TQR-TNNSR）are proposed.This method combines the sparse regularization term of SRTD and uses the three-factor tensor decomposition to solve only the minimization problem of the truncated nuclear norm of a smaller tensor,which significantly reduces the computation cost and improves the computation speed.In addition,the method does not set inner and outer iterations,so the algorithm structure is simpler than SRTD.In this thesis,the only goal is not to improve the recovery accuracy but to comprehen-sively consider the calculation accuracy and speed.The proposed completion algorithm has higher recovery accuracy and lower calculation cost and has more significant advan-tages in the processing of high-dimensional scenes.