The Study Of Matrix Completion Algorithms And Image Recovery

With the development of the technology,the scale of the data is becoming larger and larger,and the requirements and challenges for data processing are increasing gradually.Generally,data exists in the form of a matrix,and it can be said that the scale and the number of the dimension of the matrix is becoming larger and larger.However,data is often susceptible to noise or other factors during storage,transmission,compression or generation,and becomes incomplete,unreal or partially lost.The incomplete,damaged or missing data will affect the results of data analysis,so matrix completion plays a very important role in data analysis and processing.It is widely used for image inpainting,recommended system,video inpainting,machine learning,and computer vision fields.In the past twenty years,more and more scholars have studied and improved the algorithms of the matrix completion technology,but with the development of the scale and the size of the matrix,but the most existing approaches cannot applicable for large-scale and higher-order problem as the highly cost of the computational.There are two part of the matrix completion technology,the first part is extracting the characteristic form the observable elements and information in the matrix;the second part is the reconstruction of matrix.The first part determines the complexity and effect of the calculation,and the traditional method of solve the first part is principal component analysis(PCA)or the singular value decomposition(SVD),but the complexity of the computation is growing by the square of the dimension.In order to solve this problem,this paper attempts to proposes two methods,which one is based on a fast random projection algorithm for matrix completion(FRPMC),and the other is based on an orthogonal random projection algorithm for matrix completion(ORPMC).Both of them project the high-dimension data into lowdimension subspace,and then extract features from the matrix,which can greatly reduce the cost of computation and improve the efficiency for solving the problem.In order to adapt the development of the modern science and technology,we also extend an algorithm for processing high-dimensional data based on the matrix completion algorithms which are based on random projection,the algorithm is called an orthogonal random projection for tensor completion(ORPTC).In this paper,we prove that FRPMC,ORPMC and ORPTC method can effectively handle the artificial data and image data recovery via several synthetic and real data experiments.The results of FRPMC and ORPMC are better than SVT,APG,ALM and OptSpace in the real data experiments.