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We propose a novel joint compressive imaging system, which combines the merit of Single Pixel Camera (SPC) and Coded Aperture Snapshot Spectral Imaging (CASSI) system. This enables us to capture multi- or hyperspectral information with a single pixel detector. The desired 3D image cube is reconstructed by a concatenation of deep-unfolding-based algorithm and plug-and-play algorithm with deep-learning-based denoiser. We demonstrate the feasibility of the proposed system in both simulation and experiments. With advanced algorithms, the joint compressive imaging system is able to output comparable hyperspectral images with existing SD-CASSI system. Moreover, by adapting ultra-broad-spectrum photodiodes, the proposed system can be easily expanded to Near- and Mid-infrared band and thus being a low-cost approach to IR spectroscopy.