High-dimensional Image Restoration Algorithms Based On Tensor

Hyperspectral image(HSI)data have the wealth of available spectral information and widely applications.However,HSIs are unavoidably contaminated by various kinds of noise during the acquisition process,such as Gaussian noise,impulse noise,and stripes etc..These noises not only make people unable to obtain information quickly and accurately,but also affect subsequent processing and application.Various methods of high-dimensional image restoration are also emerging.The most common is tensor decomposition,which usually converts 3D to 2D,or even lower dimensionality,which will destroy the inherent structure and missing data.In this paper,we mainly use the tensor ring decomposition to study hyperspectral recovery,a series of de-noising methods for hyperspectral image are proposed.The main research work and achievements of this paper are as follows:(1)A non-local regularized hyperspectral image noise removal algorithm based on tensor ring decomposition(TRTD-NRM)is proposed.The algorithm uses the properties of tensor ring decomposition to directly process high-dimensional signals to study global spectral correlation(GCS)and spatial non-local self-similarity(NSS).The traditional CP decomposition is replaced with tensor ring decomposition,which can directly process high-dimensional images.The image structure will not be destroyed,and the internal properties and external structure of the hyperspectral image can be well preserved,and the optimal rank does not need to be estimated,which simplifies the calculation.Numerical experiments show that compared with the existing algorithms,the noise removal effect of this paper is relatively good,and the restoration effect is obvious.(2)A hyperspectral image restoration model(LTRSSTV),which combine spatial spectral total variation and low-rank tensor approximation,is proposed.This model uses tensor ring decomposition to explore the non-local self-similarity and local spectral correlation of high-dimensional data;uses the tensor kernel norm defined by non-zero singular tubes to perform low-rank tensor approximation,thereby improving the noise reduction ability of the model;And the use of spatial spectral total variation to explore the global spatial structure and the spectral correlation of adjacent bands can well retain its detailed information without changing its structure.Numerical experiments show that,compared with the four mainstream algorithms,the new model retains the image detail information better,so that the final restoration effect is obvious.