"Phase retrieval from binary questions about subspace proximity"Domel-White, DylanPhase retrieval is the task of reconstructing an unknown vector in a Hilbert space from magnitudes of linear functionals (or higher-rank orthogonal projections) applied to it. Quantized phase retrieval has been studied in recent years, with binary/one-bit quantization as the focus. We present a measurement and reconstruction algorithm for approximate phase retrieval in finite-dimensional Hilbert spaces from norms of projections after binary quantization, along with pointwise and uniform error bounds on its accuracy that improve on previous results. The binary information we measure is the answer to the question "is the unknown vector closer to a subspace V or to its orthogonal complement?" for many randomly chosen subspaces V. |
| http://univie.ac.at/projektservice-mathematik/e/talks/Domel-White_2021-07_Online ICCHA 2021 One-Page Paper - Dylan Domel-White.pdf |
« back