Spectral imaging, the sensing of spatial information as a function of wavelength, is a widely used diagnostic technique in diverse fields such as physics, chemistry, biology, medicine, astronomy, and remote sensing. In this paper, we present a novel computational imaging modality that enables high-resolution spectral imaging by distributing the imaging task between a photon sieve system and a computer. The photon sieve system, coupled with a moving detector, provides measurements from multiple planes. Then an inverse problem is solved in a Bayesian estimation framework to reconstruct the multi-spectral images from these superimposed and blurred measurements. The results illustrate that this technique enables higher spatial and spectral resolution than conventional filtered-based spectral imagers.