Phase retrieval in frame theory

Abstract

This dissertation is the study of phase retrieval in frame theory. The first part is concerned with the analysis of phase retrieval and the complete classification of norm retrieval. Norm retrieval is essential to transfer the properties of phase retrieval to the complement space. The first section includes the results regarding projections and also the characterization of phase retrieval and norm retrieval for subspaces. The second 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.