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We present a compact, diffuser assisted, single-pixel computational camera. A rotating ground glass diffuser is adopted, in preference to a commonly used digital micro-mirror device (DMD), to encode a two-dimensional (2D) image into single-pixel signals. We retrieve images with an 8.8% sampling ratio after the calibration of the pseudo-random pattern of the diffuser under light-emitting diode (LED) illumination. Furthermore, we demonstrate hyperspectral imaging with line array detection by adding a diffraction grating. As the random and fixed patterns of a rotating diffuser placed in the image plane can serve as 2D modulation patterns in single-pixel imaging, we do not need further calibration for spectral imaging case since we use a parallel recovery strategy for images at all wavelengths. The implementation results in a cost-effective single-pixel camera for high-dimensional imaging, with potential for imaging in non-visible wavebands.