Most subpixel detection approaches require either full or partial prior target knowledge. In many practical applications, such prior knowledge is generally very difficult to obtain, if not impossible. One way to remedy this situation is to obtain target information directly from the image data in an unsupervised manner. In this paper, unsupervised target subpixel detection is considered. Three unsupervised learning algorithms are proposed, which are the unsupervised vector quantization (UVQ) algorithm, unsupervised target generation process (UTGP) and unsupervised NCLS (UNCLS) algorithm. These algorithms produce necessary target information from the image data with no prior information required. Such generated target information is referred to as a posteriori target information and can be used to perform target detection.
Anomaly detection presented in this paper does not need any kind of target information. In other words, target information plays no role in anomaly detection. The purpose of our anomaly detection is to locate and search for targets which are generally unknown, but relatively small with low probabilities in an image scene. These anomalous targets cannot be identified by prior knowledge. Two approaches are considered in this paper, the RX algorithm developed by Reed and Yu and a uniform target detector (UTD) derived from the low probability detection in Harsanyi's dissertation, both of which operate a matched filter form with different matched signals used in the individual approaches. The matched signal used in the RX algorithm is the pixel vector r while the UTD using the unity vector 1 the matched signal. In addition, they both can be implemented in real-time.
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.
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