Can we beat Hadamard multiplexing? Data driven design and analysis for computational imaging systems

Computational Imaging (CI) systems that exploit optical multiplexing and algorithmic demultiplexing have been shown to improve imaging performance in tasks such as motion deblurring, extended depth of field, light field and hyper-spectral imaging. Design and performance analysis of many of these approaches tend to ignore the role of image priors. It is well known that utilizing statistical image priors significantly improves demultiplexing performance. In this paper, we extend the Gaussian Mixture Model as a data-driven image prior (proposed by Mitra et. al [21]) to under-determined linear systems and study compressive CI methods such as light-field and hyper-spectral imaging. Further, we derive a novel algorithm for optimizing multiplexing matrices that simultaneously accounts for (a) sensor noise (b) image priors and (c) CI design constraints. We use our algorithm to design data-optimal multiplexing matrices for a variety of existing CI designs, and we use these matrices to analyze the performance of CI systems as a function of noise level. Our analysis gives new insight into the optimal performance of CI systems, and how this relates to the performance of classical multiplexing designs such as Hadamard matrices.