Hyperspectral Image Recovery Based On Non-Convex Low-Rank Tensor Relaxation

Hyperspectral images(HSI)has a wide application.As the inherent structure and other factors,HSI is easy to be degraded,which further affect the subsequent processing.So,the research of HSI restoration has important significance.HSI has three dimensions,tensor can exploit the intrinsic characteristics of HSI.Therefore,low-rank tensor representation of HSI is important.Because of the various kinds of tensor decomposition,the definition and computation of tensor rank are more complex.Therefore,it is important to study the approximation of low-rank of tensor.From low-rank tensor approximation,this paper proposes a new non-convex norm of tensor,and proves its advantages in the representation of low-rank tensor.Then puts forward the model and algorithm of HSI restoration based on the proposed norm.The main works are as follows:(1)The tensor low-rank approximation based on tensor nuclear norm will over punish the large singular value,resulting in bias.Therefore,based on the minimum and maximum concave penalty function of tensor,a new relaxation γ-norm of tensor is proposed.The properties and approximation performance to rank of tensor are studied.On this basis,the non-convex soft threshold operator is proposed.(2)In order to further illustrate the low-rank approximation performance of the proposed tensor γ-norm,the following two models and algorithms are proposed in two HSI restoration scenarios.Firstly，tensor complement is utilize to model the problem of missing data in HSI.Considering the spatial spectral joint correlation of HSI,a priori constraint of low-rank tensor is introduced,and the proposed new norm is regarded as a non-convex relaxation of rank,then HSI restoration with non-convex low-rank tensor complement is proposed.Secondly,the tensor robust principal component analysis is used to remove the mixed noise.The proposed new tensor norm is introduced into robust principal com-ponent analysis as a non-convex relaxation of rank of tensor.At the same time,the sparse noise in HSI is constrained by the sparse measure of tensor.Therefore,HSI restoration based on non-convex low-rank tensor robust PCA is proposed.Both simulation and real data experiments show that the proposed methods have a better effect on image restoration.