Research has shown that a frame for an n-dimensional real Hilbert space oﬀers phase retrieval if and only if it has the complement property. There is a geometric characterization of general frames, the Han-Larson-Naimark Dilation Theorem, which gives us the necessary and suﬃcient conditions required to dilate a frame for an n-dimensional Hilbert space to a frame for a Hilbert space of higher dimension k. However, a frame having the complement property in an n-dimensional real Hilbert space does not ensure that its dilation will oﬀer phase retrieval. In this thesis, we will explore and provide what necessary and suﬃcient conditions must be satisﬁed to dilate a phase retrieval frame for an n-dimensional real Hilbert space to a phase retrieval frame for a k-dimensional real Hilbert.
Bachelor of Science (B.S.)
College of Sciences
Orlando (Main) Campus
Greuling, Jason L., "I’m Being Framed: Phase Retrieval and Frame Dilation in Finite-Dimensional Real Hilbert Spaces" (2018). Honors Undergraduate Theses. 319.