Sparse Unmixing Of Hyperspectral Images

Hyperspectral remote sensing image has high spectral resolution with each pixel records tens and hundreds bands.However,due to the relative low spatial resolution and naturally mixture of different materials,mixed pixels combined by several materials are commonly exist in hyperspectral images.Unmixing aims to extract the endmembers spectra of pure materials and estimate their abundances from the mixed pixel.Sparse unmixing becomes a popular semi-supervised unmixing method in recent years,it uses an overcomplete spectral library as the candidate set of endmembers,then combines the endmember extraction and abundance estimation in an optimization problem of solving a sparse regression function.Linear mixture model based sparse unmixing assumes mixed pixels are linear combination of several spectra in the spectral library,it uses sparse optimization algorithms to select optimal subset of endmembers from spectral library and estimate their abundances.In this thesis,we further exploit the potential prior information in unmixing problems based on the classical unmixing theories.We propose three novel models for sparse unmixing,the specific research contents and innovation points are briefly introduced as follows:1.We propose spectral similarity weighted and non-convex sparse induced abundance estimation model called SLpSU.Based on the rational assumption that the spatial struc-ture similarity of the input image and estimated abundance maps are positively related,we construct a weight matrix using local spectral similarity to constrain the abundances,making the abundance estimation process guided by the information of input data.Mean-while,we adopt the?_pnorm which is non-convex but more sparse as abundance sparsity regularization,and explain its numerical advantage in theory.Besides,we design an efficient numerical scheme for the weighted abundance constraint,which avoid time con-suming inversion of large matrix in traditional calculation methods,and provide overall algorithm based on ADMM.2.We propose a framelet decomposition based sparse unmixing model called FSU.By virtue of images have redundant representation using framelet coefficients,we utilize the framelet decomposition operator to separate the high and low frequency coefficients of hyperspectral image,then construct a new data fidelity term.Because most noise are contained in the high frequency coefficients,the split data term makes FSU model more flexible to unmix images with different level of noise by parameter adjustment,and improves the robustness of abundance estimation of large noise data.Meanwhile,we also transform the abundance sparsity regularization into framelet domain to enhance the model sparsity.We prove the existence and uniqueness of solution of FSU model,and provide an optimization algorithm based on split Bregman.3.We propose a sparse unmixing frame based on low rank data reconstruction,then construct our SULR-Re model and JSULR-Re model by incorporating low rank reconstruction constraint into classical sparse unmixing model and joint sparse unmixing model.Depart from the existing methods who enforce constraints on abundance,we regularize the abundance estimation by constrain the reconstructed image which recovered from abundance.Because the noiseless hyperspectral image has low rank property based on the linear mixture hypothesis,and we expect that the endmember spectra weighted by abundances can recover the noiseless image as much as possible.Therefore,minimizing the rank of reconstructed data is able to reduce the interference of noise during abundance estimation process.We carried sfficient unmixing experiments on rich simulated mixture data and re-al world hyperspectral images,and the unmixing results of our models are compared with that of classical unmixing methods on both visual quality of abundance maps and quantitative metrics to illustrate the effectiveness of all the proposed techniques.