Abstract: This dissertation is the study of phase retrieval in frame theory. Phase retrieval is inspired by the engineering applications in signal processing and information theory. In signal processing, phase retrieval is the problem of retrieving a phase of a signal from a set of intensity measurements.
The first part of this talk is concerned with the analysis of phase retrieval and the second part is dedicated to the classification of norm retrieval. Norm retrieval is essential to transfer the properties of phase retrieval to the complement space. Some results regarding projections and also the characterization of phase retrieval and norm retrieval for subspaces will be provided. The third part is the study of weak phase retrieval which was motivated by the idea of reducing the number of vectors satisfying the properties close to phase retrieval. The last section provides the correlation between weak phase retrieval and phase retrieval properties along with the examples illustrating the relationship between weak phase retrieval and the related concepts.
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