Hyperspectral Image Denoising Based On Low-rank Regularization In Tensor Transform Domain

Hyperspectral image（HSI）,has been widely used in agriculture,environmental monitoring,geological exploration,and other fields.However,the obtained HSI often contains noise,which has an influence on the sequence processing,such as classification,recognition,and detection.Thus,denoising has been a hot research topic.HSI contains both spatial and spectral dimension information,and has strong spatial-spectral correlation with abundance data.Therefore,by using tensor representation,this thesis aims to find out the efficient tensor low-rank regularization for HIS.Furthermore,tensor transform domain low-rank approximation is developed,and HSI denoising models and algorithms of low-rank tensor are established.The main contributions are summarized as follows:（1）To obtain more comprehensive and rich information,each modes of the hyperspectral tensor should be fully exploited.Based on the tensor singular value decomposition in an adaptive transform domain,a non-convex tensor low-rank representation in n-mode adaptive transform domain is proposed.Firstly,orthogonal transformations are performed along each mode,then a new n-mode adaptive transform domain tensor nuclear norm is defined.Secondly,combined with the non-convex relaxation of low-rank,the non-convex Gamma norm of tensor in n-mode transformation domain is proposed.Furthermore,the properties of the new tensor norm are analyzed and proved.Finally,a non-convex low-rank tensor regularized HSI denoising model is established,and the alternating direction multiplier method is used to solve the model.Compared with the existing low-rank tensor and transform domain low rank tensor methods,the proposed model can effectively remove the mixed Gaussian and impulse noise,and has better spatial structure preservation and spectral fidelity performance,as well as strong robustness and stability.（2）By taking the advantage of wavelet transform,a HSI denoising model based on low-rank Tucker decomposition in wavelet domain is proposed.Firstly,two-dimensional wavelet transform is performed on the hyperspectral tensor data along the spatial dimension to obtain a new tensor,which exhibits high correlation in wavelet domain.Then the transformed tensor is decomposed by Tucker decomposition with constrained low-rank and other priors.Finally,a new HSI denoising model based on low-rank Tucker decomposition in wavelet domain is proposed.The alternating direction multiplier method is used to solve the model.The experimental results show that the proposed model has good denoising performance for removing the mixed noise of Gaussian noise and impulse noise,and has certain advantages in the fidelity of the spectrum.