Lensless coded aperture imaging with separable doubly Toeplitz masks

In certain imaging applications, conventional lens technology is constrained by the lack of materials which can effectively focus the radiation within reasonable weight and volume. One solution is to use coded apertures –opaque plates perforated with multiple pinhole-like openings. If the openings are arranged in an appropriate pattern, the images can be decoded, and a clear image computed. Recently, computational imaging and the search for means of producing programmable software-defined optics have revived interest in coded apertures. The former state-of-the-art masks, MURAs (Modified Uniformly Redundant Arrays) are effective for compact objects against uniform backgrounds, but have substantial drawbacks for extended scenes: 1) MURAs present an inherently ill-posed inversion problem that is unmanageable for large images, and 2) they are susceptible to diffraction: a diffracted MURA is no longer a MURA. This paper presents a new class of coded apertures, Separable Doubly-Toeplitz masks, which are efficiently decodable, even for very large images –orders of magnitude faster than MURAs, and which remain decodable when diffracted. We implemented the masks using programmable spatial-lightmodulators. Imaging experiments confirmed the effectiveness of Separable Doubly-Toeplitz masks - images collected in natural light of extended outdoor scenes are rendered clearly.