Recently a spectrometer concept has been invented which uses compressive sensing in combination with photonic crystal filters. Here we present an adaption of this concept in push-broom configuration for earth observation. This implementation allows for a compact design, while maintaining a high spatial resolution and high signal-to-noise ratio compared to other traditional implementations. The photonic crystals have a unique transmission profile and act as a spectral filter, which allows for the computational reconstruction of the input spectrum with a limited number of filters. We show, using simulations, that our approach is able to reconstruct input radiance spectra with high accuracy and assess the performance for different number of filter sets. We furthermore show proof-of-principle measurements of the transmission profile of a manufactured photonic crystal. Future research will focus on the effect of noise on the reconstruction algorithm as well as further filter set optimization by combining the filter selection process with trace gas concentration retrieval.