2026-05-22T15:14:57Zhttps://keep.lib.asu.edu/oai/requestoai:keep.lib.asu.edu:node-1937392024-12-19T19:04:43Zoai_pmh:alloai_pmh:repo_items193739
https://hdl.handle.net/2286/R.2.N.193739
http://rightsstatements.org/vocab/InC/1.0/
http://creativecommons.org/licenses/by-nc-sa/4.0
2024-05
28 pages
Cosentino, Dominic
Cochran, Douglas
Crider, Lauren
Barrett, The Honors College
Electrical Engineering Program
Text
The need to recover a signal from incomplete or corrupted measurements is a central challenge in signal processing. A particular problem of this type is recovery of
a signal after its Fourier magnitude or its Fourier phase is lost. This problem has a
rich history that originated in the field of x-ray crystallography and continues to be
of substantial interest in molecular imaging and numerous other applications. It has
been observed that Fourier phase is typically more important in representing recognizable features of one-dimensional signals (e.g., audio waveforms) and two-dimensional
signals, such as images. Classical experiments illustrating this observation are reproduced in this thesis, and practical iterative algorithms for recovering a signal from
either its phase or magnitude are demonstrated. Unsurprisingly, it is typically more
difficult to compensate for the loss of phase information, and recovery of a signal
from its Fourier magnitude is seen to be less effective than recovery from its Fourier
phase. A partitioning method is introduced to improve image recovery from magnitude information, and the phase unwrapping problem for one-dimensional signals is
discussed briefly.
Phase recovery
Phase Unwrapping
Signal Reconstruction
Magnitude Recovery
Signal Phase Recovery and Unwrapping