TY - JOUR
T1 - Phase Retrieval for L2([- π, π]) via the Provably Accurate and Noise Robust Numerical Inversion of Spectrogram Measurements
AU - Iwen, Mark
AU - Perlmutter, Michael
AU - Sissouno, Nada
AU - Viswanathan, Aditya
N1 - Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2023/2
Y1 - 2023/2
N2 - In this paper, we focus on the approximation of smooth functions f: [- π, π] → C, up to an unresolvable global phase ambiguity, from a finite set of Short Time Fourier Transform (STFT) magnitude (i.e., spectrogram) measurements. Two algorithms are developed for approximately inverting such measurements, each with theoretical error guarantees establishing their correctness. A detailed numerical study also demonstrates that both algorithms work well in practice and have good numerical convergence behavior.
AB - In this paper, we focus on the approximation of smooth functions f: [- π, π] → C, up to an unresolvable global phase ambiguity, from a finite set of Short Time Fourier Transform (STFT) magnitude (i.e., spectrogram) measurements. Two algorithms are developed for approximately inverting such measurements, each with theoretical error guarantees establishing their correctness. A detailed numerical study also demonstrates that both algorithms work well in practice and have good numerical convergence behavior.
KW - Phase retrieval
KW - Ptychography
KW - Spectrogram measurements
KW - STFT magnitude measurements
KW - spectogram measurements
UR - http://www.scopus.com/inward/record.url?scp=85145395364&partnerID=8YFLogxK
UR - https://doi.org/10.1007/s00041-022-09988-6
U2 - 10.1007/s00041-022-09988-6
DO - 10.1007/s00041-022-09988-6
M3 - Article
AN - SCOPUS:85145395364
SN - 1069-5869
VL - 29
JO - Journal of Fourier Analysis and Applications
JF - Journal of Fourier Analysis and Applications
IS - 1
M1 - 8
ER -