Data recovery on a manifold from linear samples

Abstract

Data recovery on a manifold is an important problem in many applications. Many such problems, e.g. phase retrieval, matrix recovery, tensor recovery, and compressive sensing, involve solving a system of linear equations knowing that the unknowns lie on a known manifold. In this thesis, we studied the recovery of signals lying on a manifold from linear measurements. Particularly, we focus on the case where signals lying on an algebraic variety. In this thesis we give a framework to study the above problem and give general results for minimum measurement problem of manifold recovery. It is applied to a variety of linear manifold recovery problems and give minimum linear measurement numbers for different cases. Many of the above minimum measurements results can be proved to be sharp.

Date of Award	2020
Original language	English
Awarding Institution	The Hong Kong University of Science and Technology
Supervisor	Yang WANG (Supervisor)