Hyperspectral imaging has been attracting considerable interest as it provides spectrally rich acquisitions useful in several applications, such as remote sensing, agriculture, astronomy, geology and medicine. Hyperspectral devices based on compressive acquisitions have appeared recently as an alternative to conventional hyperspectral imaging systems and allow for data-sampling with fewer acquisitions than classical imaging techniques, even under the Nyquist rate. However, compressive hyperspectral imaging requires a reconstruction algorithm in order to recover all the data from the raw compressed acquisition. The reconstruction process is one of the limiting factors for the spread of these devices, as it is generally time-consuming and comes with a high computational burden. Algorithmic and material acceleration with embedded and parallel architectures (e.g., GPUs and FPGAs) can considerably speed up image reconstruction, making hyperspectral compressive systems suitable for real-time applications. This paper provides an in-depth analysis of the required performance in terms of computing power, data memory and bandwidth considering a compressive hyperspectral imaging system and a state-of-the-art reconstruction algorithm as an example. The results of the analysis show that real-time application is possible by combining several approaches, namely, exploitation of system matrix sparsity and bandwidth reduction by appropriately tuning data value encoding.