Abstract

Abstract—Optical systems which measure independent random projections of a scene according to compressed sensing (CS) theory face a myriad of practical challenges related to the size of the physical platform, photon efficiency, the need for high temporal resolution, and fast reconstruction in video settings. This paper describes a coded aperture and keyed exposure approach to compressive measurement in optical systems. The proposed projections satisfy the Restricted Isometry Property for sufficiently sparse scenes, and hence are compatible with theoretical guarantees on the video reconstruction quality. These concepts can be implemented in both space and time via either amplitude modulation or phase shifting, and this paper describes the relative merits of the two approaches in terms of theoretical performance, noise and hardware considerations, and experimental results. Fast numerical algorithms which account for the nonnegativity of the projections and temporal correlations in a video sequence are developed and applied to microscopy and short-wave infrared data. Index Terms—Compressive sensing, coded apertures, convex optimization, sparsity, coded exposure, Toeplitz matrices I.