The computed tomography imaging spectrometer (CTIS) is a snapshot capable hyperspectral camera. A diffractive optical element is used to create multiple projections of the hyperspectral data cube side by side on the image sensor. A reconstruction algorithm computes the hyperspectral image from the spatio-spectral multiplexed signal. It solves a similar problem as the reconstruction algorithms used for computed tomography scanners. We present how such a system can be realized by a parallelized approach. Several apertures are placed next to each other. Each aperture creates only one projection using a grating prism.