Stability of Phase Retrieval Problem

Palina Salanevich

doi:10.1109/SampTA45681.2019.9031013

Stability of Phase Retrieval Problem

Palina Salanevich^*

^*Corresponding author for this work

University of California at Los Angeles

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

Abstract

Phase retrieval is a non-convex inverse problem of signal reconstruction from intensity measurements with respect to a measurement frame. One of the main problems in phase retrieval is to determine for which frames the associated phaseless measurement map is injective and stable. In this paper we address the question of stability of phase retrieval for two classes of random measurement maps, namely, frames with independent frame vectors satisfying bounded fourth moment assumption and frames with no independence assumptions. We propose a new method based on the frame order statistics, which can be used to establish stability of the measurement maps for other classes of frames.

Original language	English
Title of host publication	2019 13th International Conference on Sampling Theory and Applications, SampTA 2019
Publisher	IEEE
ISBN (Electronic)	9781728137414
DOIs	https://doi.org/10.1109/SampTA45681.2019.9031013
Publication status	Published - 1 Aug 2019
Externally published	Yes
Event	13th International Conference on Sampling Theory and Applications, SampTA 2019 - Bordeaux, France Duration: 8 Jul 2019 → 12 Jul 2019

Conference

Conference	13th International Conference on Sampling Theory and Applications, SampTA 2019
Country/Territory	France
City	Bordeaux
Period	8/07/19 → 12/07/19

Keywords

Extraterrestrial measurements
Phase measurement
Stability analysis
Numerical stability
Inverse problems
Image reconstruction
Noise measurement
inverse problems
signal reconstruction
statistical analysis
vectors

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10.1109/SampTA45681.2019.9031013

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title = "Stability of Phase Retrieval Problem",

abstract = "Phase retrieval is a non-convex inverse problem of signal reconstruction from intensity measurements with respect to a measurement frame. One of the main problems in phase retrieval is to determine for which frames the associated phaseless measurement map is injective and stable. In this paper we address the question of stability of phase retrieval for two classes of random measurement maps, namely, frames with independent frame vectors satisfying bounded fourth moment assumption and frames with no independence assumptions. We propose a new method based on the frame order statistics, which can be used to establish stability of the measurement maps for other classes of frames.",

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author = "Palina Salanevich",

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day = "1",

doi = "10.1109/SampTA45681.2019.9031013",

language = "English",

booktitle = "2019 13th International Conference on Sampling Theory and Applications, SampTA 2019",

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PY - 2019/8/1

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N2 - Phase retrieval is a non-convex inverse problem of signal reconstruction from intensity measurements with respect to a measurement frame. One of the main problems in phase retrieval is to determine for which frames the associated phaseless measurement map is injective and stable. In this paper we address the question of stability of phase retrieval for two classes of random measurement maps, namely, frames with independent frame vectors satisfying bounded fourth moment assumption and frames with no independence assumptions. We propose a new method based on the frame order statistics, which can be used to establish stability of the measurement maps for other classes of frames.

AB - Phase retrieval is a non-convex inverse problem of signal reconstruction from intensity measurements with respect to a measurement frame. One of the main problems in phase retrieval is to determine for which frames the associated phaseless measurement map is injective and stable. In this paper we address the question of stability of phase retrieval for two classes of random measurement maps, namely, frames with independent frame vectors satisfying bounded fourth moment assumption and frames with no independence assumptions. We propose a new method based on the frame order statistics, which can be used to establish stability of the measurement maps for other classes of frames.

KW - Extraterrestrial measurements

KW - Phase measurement

KW - Stability analysis

KW - Numerical stability

KW - Inverse problems

KW - Image reconstruction

KW - Noise measurement

KW - inverse problems

KW - signal reconstruction

KW - statistical analysis

KW - vectors

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U2 - 10.1109/SampTA45681.2019.9031013

DO - 10.1109/SampTA45681.2019.9031013

M3 - Conference contribution

AN - SCOPUS:85082850466

BT - 2019 13th International Conference on Sampling Theory and Applications, SampTA 2019

PB - IEEE

T2 - 13th International Conference on Sampling Theory and Applications, SampTA 2019

Y2 - 8 July 2019 through 12 July 2019

ER -

Stability of Phase Retrieval Problem

Abstract

Conference

Keywords

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