Subpixel detection for hyperspectral images using projection pursuit

In this paper, we present a Projection Pursuit (PP) approach to target subpixel detection. Unlike most of developed target detection algorithms that require statistical models such as a linear mixture, the proposed PP is to project a high dimensional data set into a low dimensional data space while retaining desired information of interest. It utilizes a projection index to explore projections of interestingness. In the applications of target detection in hyperspectral imagery, an interesting structure of an image scene is the one caused by man-made targets in a large unknown background. If we assume that a large volume of image background pixels can be modeled by a Gaussian distribution via the central limit theorem, then targets can be viewed as anomalies in an image scene due to the fact that their sizes are relatively small compared to their surroundings. As a result, detecting small targets in an unknown image scene is reduced to finding the outliers or deviations from a Gaussian distribution. It is known that Skewness defined by normalized third moment of the sample distribution measures the asymmetry of the distribution and Kurtosis defined by normalized fourth moment of the sample distribution measures the flatness of the distribution. They both are susceptible to outliers. Since Gaussian distribution is completely determined by its first two moments, their skewness and kurtosis are zero. So, using skewness and kurtosis as a base to design a projection index may be effective for target detection. In order to find an optimal projection index, an evolutionary algorithm is also developed. The hyperspectral image experiments show that the proposed PP method provide an effective means for target subpixel detection.