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arXiv · 1505.05431

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
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Abstract

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.

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Daniel J. Lum, Samuel H. Knarr, John C. Howell. 2015-05-20. Fast Hadamard transforms for compressive sensing of joint systems: measurement of a 3.2 million-dimensional bi-photon probability distribution. https://doi.org/10.1364/oe.23.027636

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