Hyperspectral Anomaly Detection Using Einstein Fuzzy Computing and Quantum Neural Network

In the remote sensing (RS) field, hyperspectral imagery provides rich spectral information and facilitates numerous critical applications, such as material identification. Among these applications, hyperspectral anomaly detection (HAD) aims to detect substances whose spectral characteristics deviate from background spectra, which are termed anomalies. However, many widely used HAD algorithms in the RS community identify anomalies by relying on a ``background reconstruction'' strategy. Furthermore, the lack of prior target hyperspectrum and real-world limitations collectively reduces the spectral discrepancy between anomaly and background, limiting the performance of mainstream detections. By exploring the widely applicable fuzzy theory in the RS field, this study develops an unsupervised hybrid quantum-fuzzy multi-criteria decision framework (HyFuHAD) to detect anomalies from multiple perspectives. In our HyFuHAD, each pixel is first fuzzified using multiple HAD-based membership functions (MFs), including morphological, geometrical, and statistical MFs, to obtain various types of fuzzy degrees. Then, a multi-fuzzy-rule system, empowered by Einstein fuzzy computing, infers the classical fuzzy detection from these fuzzy degrees with sub-second-level computing. The Einstein sum and product provide significantly smoother transitions compared to typical min-max-based fuzzy ``OR'' and ``AND'' during the fuzzy matching and inference steps, thereby enabling effective detections. Moreover, a lightweight quantum defuzzifier obtains the quantum fuzzy detection from fuzzy features derived from the proposed fuzzy feature aggregation network. Experiments demonstrate that our HyFuHAD algorithm achieves state-of-the-art performance by fusing the information from the quantum and classical detectors. The demo code will be publicly available at https://github.com/IHCLab/HyFuHAD.