Low Rank Matrix Decomposition Based On R Rank Approximation And Its Application In Rail Defect Detection

As a high-dimensional data processing tool,low-rank matrix decomposition(or low-rank matrix reconstruction)is widely used in computer vision,machine learning,image processing and other fields.However,in most low-rank matrix reconstruction models,the rank of the original image is not fully considered.In general,the approximation to the original image is realized by minimizing the rank function of the low-rank matrix in the decomposition model.Since the rank function minimization cannot obtain the true rank of the original image,the low-rank matrix obtained by decomposition has limited approximation ability to the original image.In addition,it is easy to decompose some background edge texture parts into sparse matrix,which affects the application effect of the model in such fields as denoising,repair and defect detection.Therefore,this paper proposes a low-rank matrix decomposition model approximated by multiple single-rank matrices,and proposes an iterative differential peak detection method for the estimation of the number of single-rank matrices r.Finally,the proposed algorithm is applied to the actual rail defect detection.The main work is divided into three parts,as follows:(1)A low rank matrix decomposition model based on multiple single rank matrix approximation is proposed.The model decomposes the original image into the sum of multiple single rank matrices and a sparse matrix.This makes the decomposition of the components of the original matrix more feasible,and the image reconstruction of different quality can be realized according to the actual requirements.So that it can show strong flexibility and good robustness when processing complex images.Experimental results show that the proposed method is robust and flexible compared with other traditional methods.(2)The influence of r value on the model and its variation rule are discussed in depth,and an r value estimation algorithm of iterative differential peak detection method is proposed.The effectiveness of the algorithm in multiple single rank matrix approximation is proved by experiments.(3)The new algorithm model of multiple single rank matrix approximation is applied to track surface defect detection.Experiments show that the proposed low-rank matrix reconstruction algorithm based on r rank approximation has good practicability and flexibility.