In this Letter, we present a new snapshot hyperspectral (HS) camera based on a multi-aperture design. The technique uses an array of modified Fabry-Perot resonators together with a lens array in order to acquire an array of spectrally multiplexed modulated sub-images. Then the original HS image is reconstructed using a compressive sensing reconstruction algorithm. The HS camera has high optical throughput and enables acquisition of almost gigapixel HS datacubes with hundreds of spectral bands. Using our camera, we demonstrate optical compression of approximately 37:1.