Hyperspectral Image Denoising Based On Regularization Tensor Decomposition

The hyperspectral image is a kind of high-dimensional image,which can reflect the spatial information and spectral information of a real scene.Hyperspectral images combine the spectral information that represents the specific properties of the object with the spatial information that reveals its spatial geometric relations,thus providing a more multidimensional,detailed,and reliable description of the scene.Due to various uncontrollable factors in the process of image acquisition,such as sensor sensitivity,photon effect,and calibration error,noises will inevitably exist in the image.These noises seriously affect the information transmission and subsequent processing in the image and bring a negative impact on its further application in the field of vision.Image denoising,as a pre-processing step in the visual field,aims to remove the noise components in the image and recover the clean image from the observed noise image.It is an idea of hyperspectral image denoising to design appropriate regularization terms based on two prior information including nonlocal spatial self-similarity and global spectral correlation.Many hyperspectral image denoising methods extract low-rank components from images and then apply low-rank constraints to them for denoising analysis.However,some methods expand low-rank three-dimensional tensors into two-dimensional matrices or one-dimensional vectors to explore the prior information in the image,which destroys the intrinsic structural correlation of hyperspectral images and makes the prior information in the image not fully utilized,affecting the effect of the image restoration.In addition,in most low-rank denoising methods,the construction of low-rank components involves the image block matching operation and the singular value decomposition of matrices and tensors in the original high-dimensional space,which often brings a large computational burden.We propose a method to remove mixed noise from hyperspectral images based on subspace representation and weighted low-rank tensor regularization.The introduction of subspace representation makes the proposed algorithm have a lower algorithm complexity and can simplify the denoising process while removing part of the noise in the image.Specifically,the hyperspectral image is projected into a low-dimensional subspace by selecting an appropriate orthogonal matrix based on the correlation between spectral bands.To preserve the intrinsic structural correlation of hyperspectral images,the denoising process is based on low-rank tensors extracted from simplified images.The weighted low-rank tensors regularization term is introduced to represent the prior information of the subspace of simplified images,and a reasonable weighting mechanism is constructed based on the physical meaning of the nuclear norm in tensor decomposition.In addition,we design a method based on iterative minimization to solve the proposed non-convex denoising model.Experiments on simulated and real data sets show that the proposed subspace representation and weighted low-rank tensor regularization approach achieve better denoising effects in both quantitative and qualitative analysis.