Hyperspectral Band Selection And Endmember Extraction Based On N-dimensional Solid Spectral Angle

Hyperspectral remote sensing refers to remote sensing science and technology with high spectral resolution.It is obvious property is combining the spectroscopy and imaging technology together.The data cube covers the spatial information and spectral information simultaneously.In particular,a substance corresponds to a specific,continuous spectral curve.Spectral similarity metrics play an important role in the analysis of hyperspectral data.Its main purpose is to determine the similarity between the test spectrum and the reference spectrum,and finally to complete the classification of the test spectrum.The existing spectral similarity metrics mainly operate two spectra,which is to complete the one-to-one similarity measure between spectra.This kind of spectral similarity metrics with two spectra can be called the binary spectral similarity metric,among which the most representative method is the Spectral Angle Metric(SAM).SAM method calculates the angle between the two spectral vectors in the Euclidean space and the angle is used as an indicator to measure the similarity of the two spectral vectors.This method owns obvious physical meaning and can overcome the spectral amplitude variation to a certain extent and thus,it has been widely used.However,when the number of spectra increases,such binary spectral similarity metrics have to compare spectra in pairs many times.What is more,this pairwise comparison is not a direct measure of joint similarity between multiple spectra.In this paper,the SAM is generalized into N-dimensional Solid Spectral Angle(NSSA).The NSSA method breaks through the limitations of SAM and can evaluate the joint similarity of several spectra quantitatively by a single calculation.It has special meaning and function.In this paper,we focus on the NSSA method as the core,and this topic mainly focuses on the hyperspectral band selection technology and the endmember extraction.The main contents are as follows:First of all,a generalized spectral angle method,which is termed as N-dimensional Solid Spectral Angle(NSSA)is proposed to overcome the limitation of traditional binary spectral similarity metrics.NSSA is the core method throughout this paper.This method has ability to calculate the solid angle constructed by multiple spectral vectors in high dimensional Euclidean space within a single calculation,and the solid angle is used as the basis to measure the similarity between the n spectra.This method avoids a large number of comparisons between paired spectra.In addition,the geometric and physical properties of the NSSA method are discussed in detail,including multiplicative factor invariance,non-additivity,nonmonotonicity and band sequence independence.These important features provide a theoretical basis for the application of NSSA in the interpretation of hyperspectral data.In addition,the Equi-distributed Sequences quasi-Monte Carlo(ESMC)algorithm is introduced to solve the multiple integration problems in the NSSA calculation process.The NSSA method provides a reference for quantitatively measuring the similarity between multivariate spectra.Secondly,considering that current hyperspectral band selection methods are mainly based on a single band as the object-oriented,and determine the importance of the band according to its information content.This kind of methods pay too much attention to the interpretation accuracy and destroy the absorption characteristic of spectra.Therefore,the band selection method based on spectrum is discussed.Benefiting from the characteristics of NSSA,which can operate multivariate spectral vectors,this paper proposes a hyperspectral band selection method by using multivariate spectral sliding window.This method takes multiple spectra as object-oriented and does not need to rely on the whole hyperspectral data cube.The spectral absorption characteristics are reserved,and the accuracy of the hyperspectral data unmixing is improved simultaneously.Thirdly,considering the shortcomings of the multi-spectral sliding window based band selection algorithm,a new band selection algorithm based on the forward incremental Ndimensional solid spectral angles is proposed.The method is still based on NSSA theory,and the spectrum is object-oriented.It belongs to a semi-automatic band selection method.Firstly,the initial band set should be set,and then the NSSA value is judged as an indicator to select an efficient band.The method has the advantages of simple operation,high degree of automation,and can realize multi-spectral distinguishable characteristic band localization and recognition.Experimental results indicate that this method has ability to achieve the band selection result close to the exhaustive search when the initial band set is properly selected.In addition,this paper proposes a multi-spectral identification method based on the NSSA method,which uses the multivariate spectra as the object-oriented band selection method to extend to the multi-classes and spectral bundle selection problem.In practical research,due to lack of sample spectra,it could not provide accurate statistical information.Therefore,spectral identification research uses the binary spectra similarity metrics to determine the classification of the test spectrum according to the similarity between test spectra and reference spectra.However,the binary spectral similarity measure requires a multi-node hierarchical structure when dealing with multi-classes spectral recognition problems,and there exists a decision error between different levels.Therefore,two kinds of multivariate spectral identification methods based on NSSA are proposed,termed as average distance method based on NSSA(ADM-NSSA)and minimum distance method based on NSSA(MDM-NSSA).The annular spectra identification structure can extract the distinguishing feature of multi-classes spectra within a single calculation,and achieve a competitive identification accuracy close to that of the binary spectra identification with fewer bands and avoid the over-calculation of multi-nodes.Finally,the multi-factor invariance property of the NSSA method is researched and the Maximum N-dimensional Solid Spectral Angle(MNSSA)method based endmember extraction method is proposed.Ideally,a hyperspectral data cube is assumed to be a convex simplex in the high-dimensional Euclidean space,with the endmembers located at the vertexes of the convex simplex.However,affected by the shadow,topography,light intensity and other factors,there exists amplitude variability for endmembers,which submerged in the convex body.Traditional geometric endmember extraction methods could not identify such endmembers accurately.The MNSSA method searches for a set of pixels with the largest Euclidean spatial generalized spectral angle as the endmember.Compared with the traditional geometric algorithms,this algorithm has high computational complexity,but it can overcome the variance and noise interference from the spectral amplitude,and it has high accuracy of endmembers extraction.