  This paper introduces two acquisition device architectures for multispectral
compressive imaging. Unlike most existing methods, the proposed computational
imaging techniques do not include any dispersive element, as they use a
dedicated sensor which integrates narrowband Fabry-P\'erot spectral filters at
the pixel level. The first scheme leverages joint inpainting and
super-resolution to fill in those voxels that are missing due to the device's
limited pixel count. The second scheme, in link with compressed sensing,
introduces spatial random convolutions, but is more complex and may be affected
by diffraction. In both cases we solve the associated inverse problems by using
the same signal prior. Specifically, we propose a redundant analysis signal
prior in a convex formulation. Through numerical simulations, we explore
different realistic setups. Our objective is also to highlight some practical
guidelines and discuss their complexity trade-offs to integrate these schemes
into actual computational imaging systems. Our conclusion is that the second
technique performs best at high compression levels, in a properly sized and
calibrated setup. Otherwise, the first, simpler technique should be favored.
