An analysis of coded aperture acquisition and reconstruction using multi-frame code sequences for relaxed optical design constraints

We present an investigation of the performance of coded aperture optical systems where the elements of a set of binary coded aperture masks are applied over a sequence of acquired images. In particular, we are interested in investigating code sequences and image reconstruction algorithms that reduce the optical fidelity and hardware requirements for the system. Performance is jointly tied to the mask design, the image estimation algorithm, and the inherent optical response of the system. As such, we adopt a simplified reconstruction model and consider generalized optical system aberrations in designing masks used for multi-frame reconstruction of the imagery. We also consider the case of non-Nyquist sampled (aliased) imagery. These investigations have focused on using a regularized least-squares reconstruction model and mean squared error as a performance metric. Masks are found by attempting to minimize a closed form objective that predicts the mean squared error for the reconstruction algorithm. We find that even with suboptimal solutions that binary masks can be used to improve imagery over the case of an uncoded aperture with the same aberration.