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.
Bibliographical noteFunding Information:
We would like the thank Gregory A. Howland for the use of his computer code to verify our results and James Schneeloch for his contributions, theoretical discussions, and careful editing to make this a coherent article. This work was sponsored by the Air Force grant AFOSR Grant No. FA9550-13-1-0019.
© 2015 Optical Society of America.