The High-dimensional Image Recovery Of Removing Abnormal Noise

With the development of information technology,many application fields will involve the high-dimensional data,and the data which need to analysis and process is becoming more and more complicated in the structure,such as video images,medical images and hyperspectral data,etc.Tensor is an important tool,can better represent the complex relationships and essential structures existing between higher-order data.With the development of modern applications,tensor has been widely applied to various fields,such as image processing,pattern recognition,multi-task learning,spectral data,and intelligent transportation systems.However,in the process of data collection,storage,processing,transformation and transmission,as a result of acquisition system,storage system,the data processing methods,and even all kinds of unstable factors that exist in the operating environment,will make our real data which we obtained polluted by different level of noise,some leakage or abnormal values.The purpose of a tensor recovery is to maximize the information that is already known to retrieve elements that have been lost or contaminated for various reasons.Due to the characteristics of the tensor structure,we often use tensors to deal with high-dimensional data problems.The recovery of tensors is one of the hot topics in recent researches.On the basis of summarizing and inheriting the previous research results,this paper studies the problem of the tensor recovery with abnormal noise,establishes the recovery model of removing abnormal noise,and uses color images to perform numerical experiments.The main research results and innovation points obtained in this paper are:1、Square and Tukey biweight functions are used to fit the data,then we establish the recovery model of removing abnormal noise,propose the proximal and linearized block coordinate descent algorithm,and prove that this algorithm has global convergence.2、In the process of processing high-dimensional data,based on the low-rank tensor recovery theory,the sum of N low-rank tensors is used to approximate the tensor image which we need to solve,which to a certain extent maintains the relationship between the high-dimensional data.3、Numerical experiments were carried out on color images with abnormal noise to verify the validity of the proposed model and method.