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

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

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)
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

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10.23919/Eusipco47968.2020.9287698License: Unspecified

Cite this

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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",

note = "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. Perlmutter, Michael; Sissouno, Nada; Viswantathan, Aditya; and Iwen, Mark. (2021). {"}A Provably Accurate Algorithm for Recovering Compactly Supported Smooth Functions from Spectrogram Measurements{"}. In 2020 28th European Signal Processing Conference (EUSIPCO) (pp. 970-974). IEEE. https://doi.org/10.23919/Eusipco47968.2020.9287698",

year = "2021",

doi = "10.23919/Eusipco47968.2020.9287698",

language = "American English",

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

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TY - CHAP

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

N1 - 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. Perlmutter, Michael; Sissouno, Nada; Viswantathan, Aditya; and Iwen, Mark. (2021). "A Provably Accurate Algorithm for Recovering Compactly Supported Smooth Functions from Spectrogram Measurements". In 2020 28th European Signal Processing Conference (EUSIPCO) (pp. 970-974). IEEE. https://doi.org/10.23919/Eusipco47968.2020.9287698

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://doi.org/10.23919/Eusipco47968.2020.9287698

U2 - 10.23919/Eusipco47968.2020.9287698

DO - 10.23919/Eusipco47968.2020.9287698

M3 - Chapter

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

ER -

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

Abstract

Keywords

EGS Disciplines

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