38 IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, VOL. 5, NO. 1,JANUARY 2008 Automated Target Detection and Discrimination Using Constrained Kurtosis Maximization Qian Du, Senior Member, IEEE, and Ivica Kopriva, Senior Member, IEEE Abstract—Exploiting hyperspectral imagery without prior in- formation is a challenge. Under this circumstance, unsupervised target detection becomes an anomaly detection problem. We pro- pose an effective algorithm for target detection and discrimination based on the normalized fourth central moment named kurtosis, which can measure the flatness of a distribution. Small targets in hyperspectral imagery contribute to the tail of a distribution, thus making it heavier. The Gaussian distribution is completely determined by the first two order statistics and has zero kurtosis. Consequently, kurtosis measures the deviation of a distribution from the background and is suitable for anomaly/target detection. When imposing appropriate inequality constraints on the kurtosis to be maximized, the resulting constrained kurtosis maximization (CKM) algorithm will be able to quickly detect small targets with several projections. Compared to the widely used unconstrained kurtosis maximization algorithm, i.e., fast independent component analysis, the CKM algorithm may detect small targets with fewer projections and yield a slightly higher detection rate. Index Terms—Constrained kurtosis maximization (CKM), hyperspectral imagery, target classification, target detection. I. I NTRODUCTION T ARGET detection is one of the major tasks in hyperspec- tral image analysis. With very high spectral resolution, it is possible to detect targets based on the subtle spectral features. When the spatial resolution is low or the target size is relatively small compared to the spatial resolution, we must resort to spectral-analysis-based techniques. Target detection methods can be divided into two categories: supervised and unsupervised. The former relies on available target signatures, while the latter does not require prior target information. This research focuses on unsupervised target detection, which can be achieved by finding pixels with distinct spectral features from those in their neighborhood, i.e., anomalies [1]. An anomaly usually has a small size and occupies only several pixels. In general, anomaly detection seeks to find unknown targets from an unknown background. Several approaches have been proposed for this purpose. For instance, Reed and Yu [2] developed the well-known Reed-Xiaoli (RX) algorithm to analyze an image using the second-order statistics; Ashton [3] Manuscript received February 9, 2007; revised July 9, 2007. This work was supported in part by the National Geospatial-Intelligence Agency under Grant HM15810512006 and in part by the Ministry of Science, Education and Sport, Croatia, under Grant 098-0982903-2558. Q. Du is with the Department of Electrical and Computer Engineering and GeoResources Institute (GRI), High Performance Computing Collaboratory, Mississippi State University, Mississippi State, MS 39762 USA. I. Kopriva is with the Division of Laser and Atomic Research and Develop- ment, Rudjer Bo˘ skovi´ c Institute, Zagreb 10002, Croatia. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/LGRS.2007.907300 proposed an adaptive Bayesian classifier; the Projection Pursuit method developed by Ifarraguerri and Chang [4] employed the information divergence to find the best projector for anomaly detection; Chiang et al. [5] and Chang et al. [6] used skewness and kurtosis for target detection; Schweizer and Moura [7] pre- sented an anomaly detection method based on Gauss–Markov random field; Robila and Varshney [8], [9] applied independent component (IC) analysis (ICA) for target detection, which is based on the minimization of mutual information. However, these techniques are relatively time-consuming and some (e.g., the RX algorithm) can only detect anomalies but cannot dis- criminate them from each other. The goal of this research is to develop an efficient unsupervised algorithm for hyperspectral imagery, which not only quickly detects targets but also auto- matically distinguishes between them. In this research, we employ kurtosis, the most frequently used high-order moment, for unsupervised target detection. It is known that kurtosis is the normalized fourth central moment, which can measure the flatness of a probability distribution. If an image background can be modeled as a Gaussian distribu- tion, anomalies or small man-made targets can be viewed as outliers because their sizes are relatively small and spectral features are very different compared to their surroundings. Therefore, the corresponding pixels will contribute to the tail of the distribution and make it heavier. As a result, anomalies can be detected by searching the deviation from a Gaussian distribu- tion, which has zero kurtosis. In other words, anomaly detection can be achieved by searching the direction of non-Gaussianity. We found that kurtosis is sensitive to the outliers and works very efficiently in small target/anomaly detection. When the background cannot be modeled perfectly as a Gaussian distrib- ution, some background classes will be detected as well. As a preprocessing step, data need to be whitened by mean removal and decorrelation to prevent the first- and second-order statistics from interfering with the following high-order statistics-based analysis [10]. A distribution having a negative kurtosis is called “sub- Gaussian,” which is flatter than a Gaussian one; a distribution with a positive kurtosis is called “super-Gaussian,” which has a sharper peak and longer tails than a Gaussian one [10]. In general, the presence of targets in a hyperspectral image makes the distribution appear to be super-Gaussian. Thus, small targets and anomalies correspond to the directions with very large pos- itive kurtosis. Objects with large sizes are related to the kurtosis with small values, which can even be negative. To prevent classes with large kurtosis from becoming the obstacle in the target detection process, an inequality constraint on the value of kurtosis may need to be imposed. Multiple-target detection and discrimination can be achieved by using a Gram–Schmidt orthogonalization type of process. 1545-598X/$25.00 © 2007 IEEE