Inverting Spectrogram Measurements via Aliased Wigner Distribution Deconvolution and Angular Synchronization

Michael Perlmutter; Sami Merhi; Aditya Viswanathan; Mark Iwen

doi:10.1093/imaiai/iaaa023

Inverting Spectrogram Measurements via Aliased Wigner Distribution Deconvolution and Angular Synchronization

Michael Perlmutter, Sami Merhi, Aditya Viswanathan, Mark Iwen

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

<div class="line" id="line-5"> We propose a two-step approach for reconstructing a signal x ∈ &complexes; d from subsampled discrete short-time Fourier transform magnitude (spectogram) measurements: first, we use an aliased Wigner distribution deconvolution approach to solve for a portion of the rank-one matrix x̂x̂ *. Secondly, we use angular synchronization to solve for x̂ (and then for x by Fourier inversion). Using this method, we produce two new efficient phase retrieval algorithms that perform well numerically in comparison to standard approaches and also prove two theorems; one which guarantees the recovery of discrete, bandlimited signals x ∈ &complexes; d from fewer than d short-time Fourier transform magnitude measurements and another which establishes a new class of deterministic coded diffraction pattern measurements which are guaranteed to allow efficient and noise robust recovery. </div>

Original language	American English
Journal	Information and Inference: A Journal of the IMA
Volume	10
Issue number	4
DOIs	https://doi.org/10.1093/imaiai/iaaa023
State	Published - Dec 2021
Externally published	Yes

Keywords

Wigner distribution deconvolution
angular synchronization
phase retrieval
ptychography
short-time Fourier transform (STFT)
spectrogram measurements

EGS Disciplines

Mathematics

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10.1093/imaiai/iaaa023License: Unspecified

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title = "Inverting Spectrogram Measurements via Aliased Wigner Distribution Deconvolution and Angular Synchronization",

abstract = " We propose a two-step approach for reconstructing a signal x ∈ &complexes; d from subsampled discrete short-time Fourier transform magnitude (spectogram) measurements: first, we use an aliased Wigner distribution deconvolution approach to solve for a portion of the rank-one matrix {\^x}{\^x} *. Secondly, we use angular synchronization to solve for {\^x} (and then for x by Fourier inversion). Using this method, we produce two new efficient phase retrieval algorithms that perform well numerically in comparison to standard approaches and also prove two theorems; one which guarantees the recovery of discrete, bandlimited signals x ∈ &complexes; d from fewer than d short-time Fourier transform magnitude measurements and another which establishes a new class of deterministic coded diffraction pattern measurements which are guaranteed to allow efficient and noise robust recovery. ",

keywords = "Wigner distribution deconvolution, angular synchronization, phase retrieval, ptychography, short-time Fourier transform (STFT), spectrogram measurements",

author = "Michael Perlmutter and Sami Merhi and Aditya Viswanathan and Mark Iwen",

year = "2021",

month = dec,

doi = "10.1093/imaiai/iaaa023",

language = "American English",

volume = "10",

number = "4",

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TY - JOUR

T1 - Inverting Spectrogram Measurements via Aliased Wigner Distribution Deconvolution and Angular Synchronization

AU - Perlmutter, Michael

AU - Merhi, Sami

AU - Viswanathan, Aditya

AU - Iwen, Mark

PY - 2021/12

Y1 - 2021/12

N2 - We propose a two-step approach for reconstructing a signal x ∈ &complexes; d from subsampled discrete short-time Fourier transform magnitude (spectogram) measurements: first, we use an aliased Wigner distribution deconvolution approach to solve for a portion of the rank-one matrix x̂x̂ *. Secondly, we use angular synchronization to solve for x̂ (and then for x by Fourier inversion). Using this method, we produce two new efficient phase retrieval algorithms that perform well numerically in comparison to standard approaches and also prove two theorems; one which guarantees the recovery of discrete, bandlimited signals x ∈ &complexes; d from fewer than d short-time Fourier transform magnitude measurements and another which establishes a new class of deterministic coded diffraction pattern measurements which are guaranteed to allow efficient and noise robust recovery.

AB - We propose a two-step approach for reconstructing a signal x ∈ &complexes; d from subsampled discrete short-time Fourier transform magnitude (spectogram) measurements: first, we use an aliased Wigner distribution deconvolution approach to solve for a portion of the rank-one matrix x̂x̂ *. Secondly, we use angular synchronization to solve for x̂ (and then for x by Fourier inversion). Using this method, we produce two new efficient phase retrieval algorithms that perform well numerically in comparison to standard approaches and also prove two theorems; one which guarantees the recovery of discrete, bandlimited signals x ∈ &complexes; d from fewer than d short-time Fourier transform magnitude measurements and another which establishes a new class of deterministic coded diffraction pattern measurements which are guaranteed to allow efficient and noise robust recovery.

KW - Wigner distribution deconvolution

KW - angular synchronization

KW - phase retrieval

KW - ptychography

KW - short-time Fourier transform (STFT)

KW - spectrogram measurements

UR - https://doi.org/10.1093/imaiai/iaaa023

U2 - 10.1093/imaiai/iaaa023

DO - 10.1093/imaiai/iaaa023

M3 - Article

VL - 10

JO - Information and Inference: A Journal of the IMA

JF - Information and Inference: A Journal of the IMA

IS - 4

ER -

Inverting Spectrogram Measurements via Aliased Wigner Distribution Deconvolution and Angular Synchronization

Abstract

Keywords

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