Hyperspectral Image Denoising And Unmixing Based On Weighted Nuclear Norm

The hyperspectral image has the features of high spectral resolution,combining spatial image with spectral bands,which can provide rich information of the surface features.Therefore,the hyperspectral image has been widely used for geologic survey,agricultural remote sensing,and other important fileds.However,since the hyperspectral remote sensing belongs to passive spectral imaging and the corresponding platform has a high altitude,the observed hyperspectral image mays corrupted by heavy mixed noise(including the Gaussian noise,salt and pepper noise,and strip noise)subject to the atmospheric interference,instrument failure,sensor accuracy and many other factors during the image acquisition and transmission,which inevitable affects the subsequent processing and application.In addition,due to the low spatial resolution of hyperspectral image and complex distribution of the surface features,the mixed pixels in hyperspectral image are widespread and greatly affect the sub-pixel-level data processing and analysis.In order to improve the accuracy of object recognition and classification,the endmember decomposition must be performed on the mixed pixels and the abundance distribution must be obtained.This dissertation focuses on the two basic problems of hyperspectral image processing,i.e.,the mixed noise removal,and the endmember unmixing in the case of mixed noise.Several new hyperspectral image denoising and unmixing methods are proposed by utilizing both the spatial and spectral information of hyperspectral image.The main contributions and results of this dissertation can be summarized as follows:A new method for the mixed noise removal for hyperspectral image based on the weighted nuclear norm and sub-band total variation regularization(named as TV-regularized weighted nuclear norm mixed denoising,TWNNM)is proposed,aiming at the existing two problems of low rank based denoising algorithms,i.e.,the over-smoothed effect in the main singular values,and the absence of the spatial structural information.The existing methods for solving the low rank based denoising problem is the nuclear norm minimization,in which all the singular values are regularized with the same threshold value,resulting in the over-smoothed effect in the main singular values while removing the noise.This paper points out that,different singular values should be treated differently and regularized with different threshold values,so that the main singular values could be retained while removing the noise.To utilize the spatial structural information,the sub-band total variation is incorporated.A low rank optimization algorithm based on the alternating direction method of multiplier(ADMM)is also presented to solve the derived model effectively.Both simulated and real hyperspectral data experiments demonstrate that the proposed TWNNM method could effectively remove the mixed noise of hyperspectral image.A hyperspectral image mixed denoise method based on the weighted nuclear norm and structure tensor total variation regularization(named as structure tensor TV-regularized weighted nuclear norm mixed denoising,STWNNM)is proposed.In the current sub-band total variation based denoising method,there are two key issues need to be solved,one is the existing sub-band total variation could not jointly utilize the spatial structural information in all the bands,the other is the sub-band total variation could only utilize the nearby pixel information,resulting in the limited denoising performance against the wider stripe noise and the so-called ‘oil painting' effect.In the STWNNM,the structure tensor is constructed with all the band gradient images under the convolution of Gaussian kernel.Then the matrix Schatten p-norm is used to regulate the singular values of structure tensor,which could jointly utilize the spatial structural information in all the bands and the local spatial information within each band.Based on the ADMM framework,two different low rank optimization algorithms are proposed to solve the derived model,both theory analysis and experimental results show that these two optimization algorithms are identical.Then,both simulated and real hyperspectral data experimental results confirm that the STWNNM model could effectively remove the mixed noise of hyperspectral iamge.A hyperspectral image mixed denoise method based on the weighted nuclear norm and three dimensional spatial-spectral total variation regularization(named as low rank constraint and spatial spectral total variation method,LSSTV)is proposed.In the current low rank based hyperspectral denoising methods,the recovered image always suffers from the spectrum distortion due to the absence of spectral local smooth constraint.Aiming at this problem,a new hyperspectral image denoising method is proposed based on the weighted nuclear norm and three dimensional spatial-spectral total variation,by combining the global low rank constraint,the local spatial smooth constraint,and local spectral smooth constraint into the union model.Based on the ADMM framework,a low rank optimization algorithm is proposed to solve the derived model.Then,both simulated and real hyperspectral data experimental results confirm that the LSSTV method could effectively preserve the spatial and spectral local smooth properties while removing the mixed noise.A hyperspectral image sparse unmixing method in the case of mixed noise(named as coupled denoising and unmixing method,c De Un)is proposed.In the current research idea,the sparse unmixing in the case of mixed noise needs to be split into two processing steps,first one is the noise removal,and then followed by the sparse unmixing.However,this processing flow suffers from the problem that the spectrum distortion during the denoising may decrease the performance of sparse unmixing.To solve the problem,we firstly analyse the differences and similarities between the denoising and unmixing,and then propose a new processing flow,in which both the denoising and unmixing problems are combined into the union model at the mathematical form.The model consists of the weighted nuclear norm item used for denoising,the sparse item used for unmixing,and the hypergraph regularization item used for the local spatial information constraint.Based on the ADMM framework,all these three items are solved successively in the loop.All these items act as constraints to each other and the effects of them can promote each other.Both simulated and real hyperspectral data experimental results show that the c De Un method could achieve the superior unmixing performance under the case of mixed noise.