Matrix recovery from bilinear and quadratic measurements
Abstract
Matrix (or operator) recovery from linear measurements is a well-studied problem. However, there are situations where only bilinear or quadratic measurements are available. A bilinear or quadratic problem can easily be transformed into a linear one, but it raises questions when the linearized problem is solvable and what is the cost of linearization. In this work, we study a few specific cases of this general problem and show when the bilinear problem is solvable. Using this result and certain properties of polynomial rings, we present a scenario when the quadratic problem can be linearized at the cost of just a linear number of additional measurements. Finally, we link our results back to two applications that inspired it: Time Encoding Machines and Continuous Localisation.
Keywords
Cite
@article{arxiv.2001.04933,
title = {Matrix recovery from bilinear and quadratic measurements},
author = {Michalina Pacholska and Karen Adam and Adam Scholefield and Martin Vetterli},
journal= {arXiv preprint arXiv:2001.04933},
year = {2020}
}
Comments
19 pages, 4 figures, Changes since the first version: added section on TEMs, fixed typos, added and updated references