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This paper proposes a snapshot Compressed Light Field Imaging Spectrometer based on compressed sensing and light field concept, which can acquire the two-dimensional spatial distribution, depth estimation and spectral intensity of input scenes simultaneously. The primary structure of the system contains fore optics, coded aperture, dispersion element and light field sensor. The detected data can record the coded mixture spatial-spectral information of the input scene with direction information of light rays. The datacube containing depth estimation can be recovered with the compressed sensing and digital refocus framework. We establish the mathematical model of the system and conduct simulations for verification. The reconstruction strategy is demonstrated for the simulation data.