On Image Error Detection Based On Subspace Learning

Error correction is a very important topic in machine learning.The data obtained in reality contains more or less damaged parts.How to deal with this damaged da ta is a very difficult problem.People have been studying this problem for a long time.The equivalent description of this problem in mathematics is to reveal the structure of data in high-dimensional space in low-dimensional subspace.There are many machine learning methods to solve this problem,but the existing methods have certain limitations,that is,their computing performance will decrease with the increase of the dimension,and the domain structure of the original data is usually ignored.Rather,these methods are not working in the high-dimensional solution we are considering.In this paper,based on the subspace learning method,we propose a flexible robust principal component analysis(FRPCA)method.It is projected into a low-dimensional subspace by passing the original data through a reconstruction matrix,and then in this low-dimensional subspace we can separate the errors contained in the data.But unlike the traditional method of using only one reconstruction matrix,our method uses two different matrices to reconstruct the data from the original data,and can obtain a compact representation of the data by using one of the matrices.In addition,the FRPCA method selects the most relevant features to ensure that the recovered data retains the d omain structure of the original data well.For this machine learning problem,we mathematically express it,thus obtaining a convex optimization problem,and the machine learning process is completed by solving the kernel norm regularization minimization problem,and we prove that this problem can be solved in polynomial time.For the specific solution method of this convex optimization problem,we use the alternating direction multiplier method to solve.By decomposing the coordinate method,we turn the solution of the optimization problem into a solution to the smaller local sub-problems,and then solve the solutions to these large suboptimal problems in a coordinated manner.In the experimental part,in order to reflect the universality of our method,we reconstructed the target image sequence containing various environments(such as campus,laboratory,subway station,etc.).A series of data shows that our method can accurately separate the foreground and background.In the experiment of restoring face im ages,we first randomly add Gaussian noise in the complete face image data,and then use different methods to de-noise the image.The results show that in the case of adding different proportions of noise,our method always recovers the most accurate image.