Hyperspectral Image Restoration Based On Total Variation And Low Rank Decomposition

Hyperspectral images provide spectral information of hundreds of continuous bands in the same scene.It is widely used in many fields such as environmental research,agriculture,military and geography.In recent years,they have aroused great research interest in the field of remote sensing.However,due to the limitations of observation conditions and sensors,the hyperspectral image obtained by hyperspectral sensors is usually contaminated by various noises,such as Gaussian noise,stripes,dead-line and impulse noise.These noises will seriously degrade the quality of hyperspectral images and affect the accuracy of subsequent processing and applications,e.g.,feature classification,target detection,and unmixing.Therefore,to overcome the problem of noise pollution,it is necessary to preprocess the original hyperspectral image from the perspective of data to improve the quality of the data and provide data quality assurance for subsequent applications.In this paper,firstly,the major denoising models pertinent to remote-sensing are intro-duced.Based on these existing research,we further summarized the mechanisms,advantages and limitations of these methods,including natural image-based hyperspectral denoising tech-nologies,matrix based denoising technology,tensor based denoising models,deep learning based technology.Then,we summarized several problems that need to be solved urgently in the field of hyperspectral image denoising.In response to these problems,on the basis of the latest existing technologies,this paper proposed two hyperspectral image denoising models based on the theory of low rank,regularization technology and deep learning,by combin-ing mathematical theory and the actual physical structure of hyperspectral images.The core contributions of this thesis are listed as follows:（1）For hyperspectral image denoising tasks,the low-rank model based on band-by-band total variation regularization is a kind of classic method to eliminate mixed noise.Generally,the rank of a low-rank matrix is approximated by the nuclear norm,which is defined by adding all the singular values.This means the nuclear norm is essentially the L₁-norm of the singular values,which will lead to non-negligible approximating error,and make the estimated matrix may be significantly deviated from the groundtruth.In addition,the method based on total variation from band to band only explores spatial information in an independent metric.Aiming at these problems,we proposed a novel spatial-spectral total variation regularized non-convex local low-rank matrix restoration method to eliminate the hybrid noise in hyperspectral images.On the one hand,although the real hyperspectral image data is not ideally low-rank in the global range due to the existence of non-independent and differently distributed noise and outliers,the clear hyperspectral image data still owns its potential local low rank attributes.Based on this fact,we designed a new L_γnorm to represent such local low-rank prior.On the other hand,suppose that the hyperspectral image is piecewise smooth in the global spatial and spectral domain.We utilized spatial-spectral total variation regularization to explore the global spatial-spectral smoothing structure at the same time to overcome the shortcomings of the traditional 2-D total variation.Experimental results on simulated and real hyperspectral image datasets showed that the use of local low-rank matrix and global spatial-spectral total variation is beneficial to retain local details and overall structural information.（2）For the task of hyperspectral image restoration,in the flexible and scalable plug-and-play framework,a convolutional neural network based low-rank tensor approximation is proposed,which combines the best of traditional physical restoration models and convolutional neural networks.For the physical prior of hyperspectral images,low-rank tensor decomposition based on Tucker decomposition can fully explore the global correlation in the spatial and spectral domains.For implicit priors,methods based on convolutional neural networks can represent priors that cannot be designed by mathematical theory tools.We also designed an alternating direction multiplier method based algorithm to quickly solve the proposed model.Experiments with simulated data and real data show that,compared with the competing methods,the proposed method can obtain better hyperspectral image restoration performance on various quantitative evaluation indicators.