Principal kurtosis analysis and its application for remote-sensing imagery

Fast Independent Component Analysis FastICA is the commonly used feature extraction method for non-Gaussian structure data and it is often used in multispectral/hyperspectral image processing. However, FastICA requires all pixels to be involved at each iteration. Therefore, it is a very time-consuming method when the total number of iterations is large. In this study, we propose an equivalent algebraic method for FastICA when selecting kurtosis as a non-Gaussian index. We name this new method principal kurtosis analysis PKA. The feature extraction result of PKA is equivalent to that of FastICA when considering kurtosis as the measurement of non-Gaussianity. Similar to FastICA, PKA also applies the fixed-point iteration method to search for extreme kurtosis directions. However, when computing the projected direction in the iteration process, PKA only requires a co-kurtosis tensor and not all of the pixels. Therefore, this reduces the time complexity. The proposed algorithm PKA has been applied on multispectral and hyperspectral images and shows its time advantage in the experiments.