高光谱图像快速Gram行列式端元提取优化方法

Improved endmember extraction method based on fast Gram determinant analysis for hyperspectral imagery

高光谱图像快速Gram行列式端元提取算法基于高光谱图像最大单形体体积标准,具有容易理解、算法复杂度低、无需降维处理等特点,但是其在进行端元提取时,采用的计算公式仍需进行矩阵求逆,随着端元的逐个求解,矩阵维数增多导致计算量增加。由于端元提取时获得的端元Gram矩阵满足对称特性,引入埃尔米特矩阵(Hermitian matrix)分块求逆引理,简化矩阵求逆处理,优化快速Gram行列式端元提取方法。采用美国Cuprite矿区的机载可见光/红外成像光谱仪(airborne visible/infrared imaging spectrometer,AVIRIS)机载高光谱图像进行实验验证,并对该方法在不同初始化条件下的求解结果进行分析,结果表明快速Gram行列式端元提取方法会受到初始条件的影响,在端元、像元数量增加时所提方法可提升计算效率。

On the basis of the maximum volume criterion in the hyperspectral imagery,the fast Gram determinant-based endmember extraction algorithm (FGDA) has the characteristics of simplicity,low computational complexity and no dimensionality reduction needed.However,the inversion matrix needs to be calculated in the procedure of FGDA,which still leads to the expensively computational cost as the number of extracted endmembers grows.The block matrix inversion lemma is used to solve the problem due to the symmetry property of the endmember Gram matrix.The improved approach can raise the efficiency through taking advantages of the recursive relationship of the block inversion matrix.A sub-scene of airborne visible/infrared imaging spectrometer (AVIRIS) hyperspectral data collected over Cuprite mining site,Nevada,is used to validate the method and the results of different initial conditions for FGDA are also analyzed.Experimental results demonstrate FGDA is affected by its initial condition,and the proposed approach can improve the computational efficiency of FGDA as the number of endmembers and pixels in hyperspectral imagery increases.