Michalina Pacholska, Karen Adam and Martin Vetterli.
Matrix (or operator) recovery from linear measurements is a well studied problem. However, there are situations where only bi-linear or quadratic measurements are available. A bi-linear or quadratic problem can be easily transformed to 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 to two applications: mixing and continuous localisation.