PRIME: Unsupervised Multispectral Unmixing Using Virtual Quantum Prism and Convex Geometry

Multispectral unmixing (MU) is critical due to the inevitable mixed-pixel phenomenon caused by the limited spatial resolution of typical multispectral images (MSIs) in remote sensing. However, MU mathematically corresponds to the underdetermined unsupervised source separation (USS) problem, thus highly challenging, making it a daunting task for researchers to tackle it. Previous MU works all ignore the underdetermined issue and merely consider scenarios with more bands than sources. This work attempts to resolve the underdetermined issue by further conducting the light-splitting task using a network-inspired virtual prism, and as this task is challenging, we achieve so by incorporating very advanced quantum feature extraction techniques. We emphasize that the prism is virtual (allowing us to fix the spectral response as a simple deterministic matrix), so the virtual hyperspectral image (HSI) it generates does not need to correspond to some real hyperspectral sensor; in other words, it is good enough as long as the virtual HSI satisfies some fundamental properties of light splitting (e.g., nonnegativity and continuity). With the above virtual quantum prism, we know that the virtual HSI is expected to possess some desired simplex structure. This allows us to adopt the convex geometry (CG) to unmix the spectra, followed by downsampling the pure spectra back to the multispectral domain, thereby achieving MU. Experimental evidence shows the great potential of our MU algorithm, termed prism-inspired multispectral endmember extraction (PRIME).