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.
D. J. Lum, S. H. Knarr, and J. C. Howell, Fast Hadamard Transforms for Compressive Sensing of Joint Systems: Measurement of a 3.2 Million-Dimensional Bi-Photon Probability Distribution, Optics Express 23(21), 27636-27649. https://doi.org/10.1364/OE.23.027636