Abstract
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.
Thesis Completion
2018
Semester
Spring
Thesis Chair/Advisor
Han, Deguang
Degree
Bachelor of Science (B.S.)
College
College of Sciences
Department
Mathematics
Degree Program
Pure Mathematics
Location
Orlando (Main) Campus
Language
English
Access Status
Open Access
Release Date
5-1-2018
Recommended Citation
Greuling, Jason L., "I’m Being Framed: Phase Retrieval and Frame Dilation in Finite-Dimensional Real Hilbert Spaces" (2018). Honors Undergraduate Theses. 319.
https://stars.library.ucf.edu/honorstheses/319
