© 2015 IEEE.Spectral imaging is a fundamental diagnostic technique with widespread application. Conventional spectral imaging approaches have intrinsic limitations on spatial and spectral resolutions due to the physical components they rely on. To overcome these physical limitations, in this paper, we develop a novel multi-spectral imaging modality that enables higher spatial and spectral resolutions. In the developed computational imaging modality, we exploit a diffractive lens, such as a photon sieve, for both dispersing and focusing the optical field, and achieve measurement diversity by changing the focusing behavior of this lens. Because the focal length of a diffractive lens is wavelength-dependent, each measurement is a superposition of differently blurred spectral components. To reconstruct the individual spectral images from these superimposed and blurred measurements, model-based fast reconstruction algorithms are developed with deep and analytical priors using alternating minimization and unrolling. Finally, the effectiveness and performance of the developed technique is illustrated for an application in astrophysical imaging under various observation scenarios in the extreme ultraviolet (EUV) regime. The results demonstrate that the technique provides not only diffraction-limited high spatial resolution, as enabled by diffractive lenses, but also the capability of resolving close-by spectral sources that would not otherwise be possible with the existing techniques. This work enables high resolution multi-spectral imaging with low cost designs for a variety of applications and spectral regimes.