PRIME: Blind 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 in remote sensing. However, MU mathematically corresponds to the underdetermined blind source separation problem, thus highly challenging, preventing researchers from tackling 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 the 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 has no 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., non-negativity 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 to unmix the spectra, followed by downsampling the pure spectra back to the multispectral domain, thereby achieving MU. Experimental evidence shows great potential of our MU algorithm, termed as prism-inspired multispectral endmember extraction (PRIME).