A Unified Multi-Target Clever Eye Algorithm: Analytical Solutions and Application - Lei Wang; Xiurui Geng; Luyan Ji (Remote Sensing)
The clever eye (CE) algorithm has been introduced for target detection in remote sensing image processing. It originally proposes the concept of data origin and can achieve the lowest average output energy compared to both the classical constrained energy minimization (CEM) and matched filter (MF) methods. In addition, it has been theoretically proven that the solutions of the best data origins can be attributed to solving a linear equation, which makes it computationally efficient. However, CE is only designed for single-target detection cases, while multiple-target detection is more demanding in real applications. In this paper, by naturally extending CE to a multiple-target case, we propose a unified algorithm termed multi-target clever eye (MTCE). The theoretical results in CE prompt us to consider an interesting question: do the MTCE solutions also share a similar structure to those of CE? Aiming to answer this question, we investigate a class of unconstrained non-convex optimization problems, where both the CE and MTCE models serve as special cases, which, interestingly, can also be utilized to solve a more generalized linear system. In addition, we further prove that all these solutions are globally optimal. In this sense, the analytical solutions of this generalized model can be deduced. Therefore, a unified framework is provided to deal with such a non-convex optimization problem, where both the solutions of MTCE and CE can be succinctly derived. Furthermore, its computational complexity is of the same magnitude as that of the other multiple-target-based methods. Experiments on both simulations and real hyperspectral remote sensing data verify our theoretical conclusions, and the comparison of quantitative metrics also demonstrates the advantage of our proposed MTCE method in multiple-target detection.