Hyperspectral Image Denoising Based On Group Sparse Nonnegative Matrix Factorization

Hyperspectral image(HSI)contains numerous narrow spectral bands of the same spatial area.It is a three-dimensional datacube consisting of two-dimensional spatial information and one-dimensional spectral information.HSI has been widely used in various fields,such as environment monitoring,geological survey and so on.However,noise is inevitably introduced into HSI during the image acquiring process,which degrades the image quality and has a negative influence on subsequent applications.Thus,HSI denoising is a significant image preprocessing step.In recent years,HSI denoising methods using low rank representation and sparse coding have attracted much attention.In the HSI,there exists strong local correlations between spectral signatures within each full-band patch(FBP),i.e.,the subcube containing the same area of all spectral bands,and adjacent spectral bands are also highly correlated.All of this suggests that spectral signatures within a clean FBP can be represented by a small number of bases.The nonlocal similarity,referring to the observation that a local patch can have many similar patches across the whole image,also exists in HSI.Denoising nonlocal similar FBPs jointly is beneficial as extra structure information is brought by the spatial self-similarity.However,as the FBPs come from different spatial locations,there may exist variations among nonlocal similar FBPs.Therefore,we propose a novel HSI denoising method based on group sparse nonnegative matrix factorization(GSNMF)to simultaneously reflect the correlation and variation mentioned above.In GSNMF,spectral signatures from nonlocal similar FBPs are assumed to be represented by a small number of bases and the coefficients of linear combination are sparse in nature.Each FBP in HSI corresponds to one group in GSNMF,and with the group sparse regularization term,spectral signatures within an FBP share a common set of bases for reconstruction,indicating the strong local correlation.In the meantime,spectral signatures across different nonlocal similar FBPs partially share a set of bases,which means that each of them may remain some non-shared bases.Thus,both nonlocal correlation and variation is considered.As a result,with the help of GSNMF,both shared and non-shared structures in HSI are captured.In this dissertation,we firstly establish the noise model,including the Gaussian noise model and mixed Poisson-Gaussian noise model.For the mixed Poisson-Gaussian noise,we use variance-stabilizing transform(VST)to convert the Poisson-Gaussian noise to the approximation of Gaussian noise.We then give concrete procedure of our proposed GSNMF-based denoising method based on the observation of the intrinsic structure of HSI.We proposed three kinds of optimization algorithms for the GSNMF model.Both basic theoretical derivation and algorithmic steps of the three algorithms are given and the computational efficiency of the three is compared in the experiments.Finally,we compared our proposed method with three other relevant HSI denoising methods on both synthetic and real hyperspectral data.The experimental results validate the effectiveness of our method.