Multispectral imaging is an important tool for understanding composite materials in many disciplines. Spectral unmixing enables the determination of individual fluorophore distributions. Due to the dispersive nature of biomaterials the observed spectra of fluorescent dyes is unknown. Spectral unmixing can be accomplished for unknown endmember spectra using minimum volume simplex analysis (MVSA). Compressive sampling (CS) is a method to reduce the computational cost of operating on sparse data sets and can be performed efficiently using NESTA based on Nesterov's algorithm. Here we demonstrate that NESTA and MVSA can be combined with a denoising threshold to create a compressive sampling and multispectral unmixing (CSMIU) method that enables efficient bioimaging and unmixing with high levels of accuracy (spectral angle distances (SADs) < 0.05). This CSMIU method may potentially enable broadband and in vivo bioimaging modalities.
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