Embodiments of the present invention relate to systems and methods for spectral imaging. In one embodiment, an image of the scene is formed on a coded aperture of a spectrometer. A coded image from the coded aperture is detected on a two-dimensional detector array of the spectrometer through a spectrally dispersive element of the spectrometer. Data from the two-dimensional detector array is collected as the coded image is varied over time. The spectral image is estimated from the data collected and the variation of the coded image over time. The data collected is varied over time through translation, rotation, and defocus.