Physical Sciences and Mathematics Commons^™

Fast Hadamard Transforms For Compressive Sensing Of Joint Systems: Measurement Of A 3.2 Million-Dimensional Bi-Photon Probability Distribution, Daniel J. Lum, Samuel H. Knarr, John C. Howell

Mathematics, Physics, and Computer Science Faculty Articles and Research

We demonstrate how to efficiently implement extremely high-dimensional compressive imaging of a bi-photon probability distribution. Our method uses fast-Hadamard-transform Kronecker-based compressive sensing to acquire the joint space distribution. We list, in detail, the operations necessary to enable fast-transform-based matrix-vector operations in the joint space to reconstruct a 16.8 million-dimensional image in less than 10 minutes. Within a subspace of that image exists a 3.2 million-dimensional bi-photon probability distribution. In addition, we demonstrate how the marginal distributions can aid in the accuracy of joint space distribution reconstructions.