Recursive Hyperspectral Band Processing for Passive Target Detection: Anomaly Detection

Abstract

Anomaly detection (AD) is studied extensively in Chaps. 5 and 14–18 in Chang (Real time progressive hyperspectral image processing: endmember finding and anomaly detection, New York, 2016), where the main focus of AD is on the design and development of AD algorithms for causal processing, which is a prerequisite for real-time processing. Chapter 6 in this book makes use of causality to further develop various real-time processing versions of AD so that AD can be carried out according to the band-interleaved-pixel/sample (BIP/BIS) data acquisition format sample by sample recursively in real time. This chapter follows Chap. 13 to look into the causality required for AD to be implemented in band processing from a band-sequential (BSQ) format perspective rather than sample processing, as described in Chap. 6 from a BIP/BIS data acquisition format perspective. Since anomalies are generally unknown and cannot be inspected by prior knowledge, their presence can only be detected by an unsupervised means. Also, because different anomalies respond to certain specific bands in terms of their own unique spectral characteristics, finding anomalies via band processing becomes a necessity. In particular, there may be anomalies that can be detected only in a small range of spectral wavelengths but may be overwhelmed by the entire wavelength coverage. In this case, detecting these anomalies using full band information may be ineffective. The progressive profiles of band-by-band detection maps offer a great value to image analysts for finding such anomalous targets. To address this issue, progressive hyperspectral band processing of anomaly detection (PHBP-AD), recently developed by Chang et al. (Progressive band processing of anomaly detection. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing 8(7): 3558–3571, 2015c), allows AD to be performed progressively band by band so as to provide progressive detection maps of anomalies band by band, a task that cannot be accomplished by any AD reported in the literature using full band information. Similar to the causal sample correlation matrix (CSCRM) introduced in Chaps. 5 and 6, we also introduce a new concept, causal band correlation matrix (CBCRM), to replace the global sample correlation matrix R. Like CSCRM, CBCRM is a correlation matrix formed by only those bands that had already been visited up to the band currently being processed but not bands yet to be visited. In this case, CBCRM must be updated repeatedly as new bands come in. To address this issue, PHBP-AD is further extended to recursive hyperspectral band processing of anomaly detection (RHBP-AD) in a manner similar to how Kalman filtering operates where results can be updated by recursive equations that only contain innovation information provided by new information but not in already processed information. Consequently, RHBP-AD not only can be carried out band by band progressively without waiting for all bands to be completed, as can PHBP-AD, but it can also process data recursively to significantly reduce computational complexity and computer process time. This great advantage allows AD to be implemented in real time in the sense of progressive as well as recursive band processing with data being processed taking place at the same time data are being collected. The progressive and recursive capability of RHBP-AD makes AD feasible for use in future satellite data communication and transmission where the data can be processed and downlinked from satellites band by band simultaneously.