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

Target detection is a fundamental task of hyperspectral imaging where constrained energy minimization (CEM) has been widely used for subpixel target detection techniques. 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), and hierarchical CEM (HCEM). Unfortunately, these generalizations overlooked the key design rationale behind CEM. This article 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, and HCEM can be generalized to iterative KCEM (IKCEM), iterative KTCIMF (IKTCIMF), iterative ECEM (IECEM), and 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 IRTS KCEM (IRTS-KCEM), IRTS ECEM (IRTS-ECEM), and IRTS 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.