基于峭度指标的FastICA算法具有较快的收敛速度和较高的计算效率，被广泛应用于多光谱图像的特征提取。经典的FastICA算法基于固定点迭代法得到图像的各个独立成分，在迭代过程中，每一个独立成分的求解都需要所有像元的参与。因此，当数据量较大或图像中像元较多时，FastICA的计算量很大，此时它的速度优势就会大打折扣。遥感数据一般都具有较大的尺寸，因此如何将FastICA直接应用于遥感数据，是一个具有实际意义的问题。通过引入多光谱图像协峭度张量的概念，将FastICA的固定点迭代问题转化为代数形式的张量计算，避免每次迭代过程中需所有像元参与的缺陷，因而大大降低计算复杂度。多光谱图像实验结果表明，该算法明显快于传统的基于峭度指标的FastICA算法。
Independent component analysis (ICA) is a popular signal processing method based on the high-order statistical characteristics of data. It has been widely used in imagery processing. However, classical FastICA algorithm achieves independent components (ICs) of the data by the fixed-point iteration method. It needs cyclic iterations to get every IC, and in the iterative process the solution of each IC requires the participation of all pixels. Therefore, when the amount of data or the number of pixels is large, FastICA is time-consuming. At this point, its speed advantage is greatly reduced. The remote sensing data generally has a large size. So how to directly apply FastICA to remote sensing data is a practical problem. In this study, by introducing the cokurtosis tensor, the fixed point iteration problem of FastICA is transformed into tensor computation in algebraic form, and the participation of all pixels is avoided, thus greatly reducing the computational complexity. Experimental results for multispectral images show that the proposed algorithm is faster than the classical FastICA algorithm based on kurtosis.
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