MF is always superior to CEM

TL;DR

This paper proves that the classical matched filter (MF) always outperforms the constrained energy minimization (CEM) in target detection, establishing their mathematical equivalence and demonstrating MF's superiority.

Contribution

The paper introduces an augmented CEM (ACEM) and proves its equivalence to MF, showing MF's consistent superiority over CEM in detection performance.

Findings

MF is mathematically equivalent to ACEM

ACEM outperforms CEM in detection tasks

MF always yields better results than CEM

Abstract

The constrained energy minimization (CEM) and matched filter (MF) are two most frequently used target detection algorithms in the remotely sensed community. In this paper, we first introduce an augmented CEM (ACEM) by adding an all-one band. According to a recently published conclusion that CEM can always achieve a better performance by adding any linearly independent bands, ACEM is better than CEM. Further, we prove that ACEM is mathematically equivalent to MF. As a result, we can conclude that the classical matched filter (MF) is always superior to the CEM operator.