Embodiments of the present invention can estimate an image using an encodement provided by an optical component, an encodement provided by a detector array, or both an encodement provided by an optical component and an encodement provided by a detector array. The original image can be encoded with a dispersed point spread function created by the optical component. The detector array can be encoded with a pixel sampling function. The encoded image is measured using the detector array. An estimated image can be calculated from the pixel sampling function and the measured image, the dispersed point spread function and the measured image, or the dispersed point spread function, the pixel sampling function, and the measured image. The number of pixels in the estimated image is greater than the number of measurements in the measured image.