Constrained Energy Minimization (CEM) for Hyperspectral Target Detection: Theory and Generalizations

Abstract

Target detection is a fundamental task of hyperspectral imaging where constrained energy minimization (CEM) has been widely used for subpixel target detection technique. Due to its effectiveness, CEM has been generalized to various versions, such as kernel CEM (KCEM), kernel target constrained interference-minimized filter (KTCIMF), ensemble cascaded CEM (ECEM), hierarchical CEM (HCEM). Unfortunately, these generalizations overlooked the key design rationale behind CEM. This paper revisits CEM for hyperspectral target detection (HTD) and proves how and why it works mathematically. Specifically, several new CEM generalizations are derived and particularly noteworthy. By including spatial information in an iterative process, KCEM, ECEM, HCEM can be generalized to iterative KCEM (IKCEM), iterative KTCIMF (IKTCIMF), iterative ECEM (IECEM), iterative HCEM (IHCEM). Also, by utilizing an iterative random training sampling (IRTS) to generate the desired target signature to be detected, these algorithms are further generalized to iterative random training sampling KCEM (IRTS-KCEM), iterative random training sampling ECEM (IRTS-ECEM), iterative random training sampling HCEM (IRTS-HCEM). A comprehensive analysis along with comparative study on these generalizations is conducted through extensive experiments to demonstrate the effectiveness of IKCEM, IHCEM and IECEM.