Abstract: A method of imaging encodes light from a scene by adding projective codes expressed as a product of a known projective code matrix with a known reconstruction matrix representing an image reconstruction operation. The encoded light is detected at a photodetector. The measurements are processed by compressive sensing including projective sub-sampling to represent the measurements as a linear system. The linear system is expressed as a plurality of undetermined linear equations including a product of the known reconstruction matrix and an unknown sparse vector. The sparse vector is approximated to provide solutions to the undetermined linear equations. At least one of a reconstructed image and an exploited image is generated from the measurements using solutions to the undetermined linear equations, wherein a product of the known reconstruction matrix with the solutions to underdetermined linear equations provides an image representation of the scene of interest having N pixels, where N>k.