Hyperspectral imaging is a major tool in modern science, which relies on a compromise between spatial resolution, spectral resolution, and imaging speed. Inspired by single-pixel imaging, we propose a versatile system that enables the fast acquisition of highspectral-resolution hypercubes. Our computational hyperspectral imaging device is composed of a compact fiber spectrometer and a digital micromirror device (DMD). By uploading a set of Hadamard patterns onto the DMD, our system acquires 64 × 64 × 2048 pixel hypercubes with a spectral resolution of 2.3 nm in less that 2 s. We show that this time can be further reduced by reconstructing hypercubes from accelerated acquisitions that exploit only a few DMD patterns. In particular, we demonstrate that a deep expectation maximization network (EM-Net) can solve this inverse problem for several acceleration factors. 8-fold acceleration enables the achievement of reconstructions with moderate spatial degradation for low frequency images. Our system allows a high degree of flexibility in the choice of spatial resolution and imaging speed, which can be easily adapted to the target application. To foster research in this field, we have made our image reconstruction algorithms, acquisition software, and several raw datasets publicly available.