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Sparsely-sampled hyperspectral stimulated Raman scattering microscopy: a theoretical investigation

A hyperspectral image corresponds to a data cube with two spatial dimensions and one spectral dimension. Through linear un-mixing, hyperspectral images can be decomposed into spectral signatures of pure components as well as their concentration maps. Due to this distinct advantage on component identification, hyperspectral imaging becomes a rapidly emerging platform for engineering better medicine and expediting scientific discovery. Among various hyperspectral imaging techniques, hyperspectral stimulated Raman scattering (HSRS) microscopy acquires data in a pixel-by-pixel scanning manner. Nevertheless, current image acquisition speed for HSRS is insufficient to capture the dynamics of freely moving subjects. Instead of reducing the pixel dwell time to achieve speed-up, which would inevitably decrease signal-to-noise ratio (SNR), we propose to reduce the total number of sampled pixels. Location of sampled pixels are carefully engineered with triangular wave Lissajous trajectory. Followed by a model-based image in-painting algorithm, the complete data is recovered for linear unmixing. Simulation results show that by careful selection of trajectory, a fill rate as low as 10% is sufficient to generate accurate linear unmixing results. The proposed framework applies to any hyperspectral beam-scanning imaging platform which demands high acquisition speed.