Constrained Energy Minimization Anomaly Detection for Hyperspectral Imagery via Dummy Variable Trick

Abstract

CEM has shown great success in subpixel target detection. This article develops a DVT to extend CEM to CEM-AD and shows that CEM-AD also enjoys the same success in anomaly detection (AD). Its idea converts a known specific target signature <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$d$ </tex-math></inline-formula> imposed on CEM into an unknown specific target signature to develop an SBR-CEM as a UST-CEM which serves as a liaison to derive the desired CEM-AD without prior knowledge of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$d$ </tex-math></inline-formula> . Surprisingly, the derived CEM-AD turns out to be a sample correlation matrix <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$R$ </tex-math></inline-formula> -based AD, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$R$ </tex-math></inline-formula> -AD in correspondence to the well-known sample covariance matrix <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> -based AD developed by Reed-Xiaoli, RX-AD. To further improve CEM-AD, an LRaSMD model introduced by GoDec and its SC are further incorporated into CEM-AD where two new versions of SC, FSC and VSC, are particularly designed to enhance AD. Finally, to effectively evaluate AD performance, recently developed 3-D ROC curve-derived detection measures are used for comparative studies and analyses.