Functional Data Analysis Method And Its Application In Hyperspectral Image Target Detection

Functional data analysis method is a new branch of statistics,whose research object is continuous data.It has important theoretical value and broad application prospects.While providing abundant spectral information,hyperspectral images have features such as high dimensionality,strong correlation,and high redundancy,which bring challenges to traditional hyperspectral images target detection.In this thesis,based on the study of functional data analysis methods,combine the characteristics of hyperspectral images and convert hyperspectral image pixels' discrete data to functional data.Furthermore,feature extraction is executed with functional data analysis methods and a new hyperspectral image target detection algorithm based on that is established.First of all,select the cubic B-spline as the basis function,simultaneously,apply the rough penalty method to smooth and solve the coefficients of the basic function expansion.Then,we can construct a functional data representation model of hyperspectral images based on cubic B-spline and the rough penalty method.This model makes full use of the rich spectral information of hyperspectral images and represents the original hyperspectral discrete data in the form of a function.Secondly,on the basis of the canonical correlation analysis method,a smooth functional canonical correlation analysis method is introduced and applied to the converted hyperspectral image functional data.The feature extraction method of hyperspectral image based on the smooth functional canonical correlation analysis method is discussed.By using the basis function method,the eigenvalues of the covariance function and the corresponding eigenvectors are solved to obtain the canonical correlation coefficients and canonical variables of the smooth functional canonical correlation analysis method,which solved the high dimensionality,strong correlation and high redundancy of the hyperspectral images.Furthermore,based on the canonical variable pairs obtained by the smooth functional canonical correlation analysis method,the background dictionary in the Sparse Matched Subspace Detector of hyperspectral images is designed.And in the case that the target dictionary is a local dictionary or a global dictionary,we establish the hyperspectral image sparse matched subspace detector model which is based on the smooth functional canonical correlation analysis.Finally,in the RIT self-test hyperspectral image database,the validity of the proposed target detection algorithm is verify and the comparison analysis of different algorithms is performed.The experiments show that the proposed algorithm is superior to the other ones.Summarize the main work of this article and take the next research direction into consideration.