A Provably Accurate Algorithm for Recovering Compactly Supported Smooth Functions from Spectrogram Measurements

Michael Perlmutter; Nada Sissouno; Aditya Viswantathan; Mark Iwen

doi:10.23919/Eusipco47968.2020.9287698

A Provably Accurate Algorithm for Recovering Compactly Supported Smooth Functions from Spectrogram Measurements

Michael Perlmutter
, Nada Sissouno
, Aditya Viswantathan
, Mark Iwen

Michigan State University
Technical University of Munich
Helmholtz Centre for Environmental Research
University of Michigan, Dearborn

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

2 Scopus citations

Abstract

We present an algorithm which is closely related to direct phase retrieval methods that have been shown to work well empirically [1], [2] and prove that it is guaranteed to recover (up to a global phase) a large class of compactly supported smooth functions from their spectrogram measurements. As a result, we take a first step toward developing a new class of practical phaseless imaging algorithms capable of producing provably accurate images of a given sample after it is masked by just a few shifts of a fixed periodic grating.

Original language	American English
Title of host publication	2020 28th European Signal Processing Conference (EUSIPCO)
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	970-974
Number of pages	5
ISBN (Electronic)	978-9-0827-9705-3
ISBN (Print)	978-9-08279-704-6, 978-1-7281-5001-7
DOIs	https://doi.org/10.23919/Eusipco47968.2020.9287698
State	Published - 2021
Externally published	Yes

Keywords

Short Time Fourier Transform (STFT) magnitude measurements
coded diffraction patterns
phase retrieval
phaseless imaging
spectogram inversion

EGS Disciplines

Mathematics

Access to Document

10.23919/Eusipco47968.2020.9287698License: Unspecified

Cite this

@inproceedings{1335197d89fa45f78b7eb090b8220485,

title = "A Provably Accurate Algorithm for Recovering Compactly Supported Smooth Functions from Spectrogram Measurements",

abstract = " We present an algorithm which is closely related to direct phase retrieval methods that have been shown to work well empirically [1], [2] and prove that it is guaranteed to recover (up to a global phase) a large class of compactly supported smooth functions from their spectrogram measurements. As a result, we take a first step toward developing a new class of practical phaseless imaging algorithms capable of producing provably accurate images of a given sample after it is masked by just a few shifts of a fixed periodic grating.",

keywords = "Short Time Fourier Transform (STFT) magnitude measurements, coded diffraction patterns, phase retrieval, phaseless imaging, spectogram inversion",

author = "Michael Perlmutter and Nada Sissouno and Aditya Viswantathan and Mark Iwen",

year = "2021",

doi = "10.23919/Eusipco47968.2020.9287698",

language = "American English",

isbn = "978-9-08279-704-6",

pages = "970--974",

booktitle = "2020 28th European Signal Processing Conference (EUSIPCO)",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

address = "United States",

}

A Provably Accurate Algorithm for Recovering Compactly Supported Smooth Functions from Spectrogram Measurements. / Perlmutter, Michael; Sissouno, Nada; Viswantathan, Aditya et al.
2020 28th European Signal Processing Conference (EUSIPCO). Institute of Electrical and Electronics Engineers Inc., 2021. p. 970-974.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - A Provably Accurate Algorithm for Recovering Compactly Supported Smooth Functions from Spectrogram Measurements

AU - Perlmutter, Michael

AU - Sissouno, Nada

AU - Viswantathan, Aditya

AU - Iwen, Mark

PY - 2021

Y1 - 2021

N2 - We present an algorithm which is closely related to direct phase retrieval methods that have been shown to work well empirically [1], [2] and prove that it is guaranteed to recover (up to a global phase) a large class of compactly supported smooth functions from their spectrogram measurements. As a result, we take a first step toward developing a new class of practical phaseless imaging algorithms capable of producing provably accurate images of a given sample after it is masked by just a few shifts of a fixed periodic grating.

AB - We present an algorithm which is closely related to direct phase retrieval methods that have been shown to work well empirically [1], [2] and prove that it is guaranteed to recover (up to a global phase) a large class of compactly supported smooth functions from their spectrogram measurements. As a result, we take a first step toward developing a new class of practical phaseless imaging algorithms capable of producing provably accurate images of a given sample after it is masked by just a few shifts of a fixed periodic grating.

KW - Short Time Fourier Transform (STFT) magnitude measurements

KW - coded diffraction patterns

KW - phase retrieval

KW - phaseless imaging

KW - spectogram inversion

UR - https://www.scopus.com/pages/publications/85099286175

U2 - 10.23919/Eusipco47968.2020.9287698

DO - 10.23919/Eusipco47968.2020.9287698

M3 - Conference contribution

SN - 978-9-08279-704-6

SN - 978-1-7281-5001-7

SP - 970

EP - 974

BT - 2020 28th European Signal Processing Conference (EUSIPCO)

PB - Institute of Electrical and Electronics Engineers Inc.

ER -

A Provably Accurate Algorithm for Recovering Compactly Supported Smooth Functions from Spectrogram Measurements

Abstract

Keywords

EGS Disciplines

Access to Document

Other files and links

Fingerprint

Cite this