THESIS
2020
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....[
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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.
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