Non-convex Phase Retrieval of Low-Rank Matrix Columns

Namrata Vaswani; Seyedehsara Nayer; Yonina C. Eldar

Non-convex Phase Retrieval of Low-Rank Matrix Columns

Namrata Vaswani, Seyedehsara Nayer, Yonina C. Eldar

Research output: Contribution to conference › Paper › peer-review

Abstract

We study the problem of recovering a low-rank matrix, X, from phaseless measurements of random linear projections of its columns. In earlier work, we introduced a novel solution approach, called AltMinTrunc, that consisted of a two-step truncated spectral initialization step, followed by a three-step alternating minimization algorithm. In this work, we obtain high probability sample complexity bounds for the AltMinTrunc initialization to provide a good approximation of thetrueX for a specific class of random matrices X. When the rank of X is low enough, these are significantly smaller than what existing single vector phase retrieval algorithms need.

Original language	English
Number of pages	5
State	Published - Dec 2016
Externally published	Yes
Event	30th Conference on Neural Information Processing Systems (NIPS 2016) - Centre Convencions Internacional Barcelona, Barcelona, Spain Duration: 5 Dec 2016 → 10 Dec 2016

Conference

Conference	30th Conference on Neural Information Processing Systems (NIPS 2016)
Country/Territory	Spain
City	Barcelona
Period	5/12/16 → 10/12/16

Access to Document

https://88a73fdb-a-62cb3a1a-s-sites.googlegroups.com/site/nonconvexnips2016/files/Paper11.pdf?attachauth=ANoY7crjtjpG0WScpQYd2fuEGfT6OjMqiOppauF7VxhgV6D2lnIw146xTyy_ffukR9YhIdctUvot507lQkDv_mVj8SjOvCN5GKYO00m0NhYW4y61wezN0wHM1jduidVoxkLgx1j9Ga1DX7v0vYEzQVdPEj7FZ7ty3j2VjvSEj1M8TkW-hR4-4r3cOKcTRFKwkU39DhS2Ssmr6IOSzV98kBSL1AH5EiPPAY6xMeGnEWGplMnsggjV6do%3D&attredirects=0License: Unspecified

Cite this

Vaswani, N., Nayer, S., & Eldar, Y. C. (2016). Non-convex Phase Retrieval of Low-Rank Matrix Columns. Paper presented at 30th Conference on Neural Information Processing Systems (NIPS 2016), Barcelona, Spain. https://88a73fdb-a-62cb3a1a-s-sites.googlegroups.com/site/nonconvexnips2016/files/Paper11.pdf?attachauth=ANoY7crjtjpG0WScpQYd2fuEGfT6OjMqiOppauF7VxhgV6D2lnIw146xTyy_ffukR9YhIdctUvot507lQkDv_mVj8SjOvCN5GKYO00m0NhYW4y61wezN0wHM1jduidVoxkLgx1j9Ga1DX7v0vYEzQVdPEj7FZ7ty3j2VjvSEj1M8TkW-hR4-4r3cOKcTRFKwkU39DhS2Ssmr6IOSzV98kBSL1AH5EiPPAY6xMeGnEWGplMnsggjV6do%3D&attredirects=0

@conference{cd43be2d9ca8477fb6dda4c2126fdb11,

title = "Non-convex Phase Retrieval of Low-Rank Matrix Columns",

abstract = "We study the problem of recovering a low-rank matrix, X, from phaseless measurements of random linear projections of its columns. In earlier work, we introduced a novel solution approach, called AltMinTrunc, that consisted of a two-step truncated spectral initialization step, followed by a three-step alternating minimization algorithm. In this work, we obtain high probability sample complexity bounds for the AltMinTrunc initialization to provide a good approximation of thetrueX for a specific class of random matrices X. When the rank of X is low enough, these are significantly smaller than what existing single vector phase retrieval algorithms need.",

author = "Namrata Vaswani and Seyedehsara Nayer and Eldar, \{Yonina C.\}",

note = "Presented at NIPS 2016 Workshop on Nonconvex Optimization for Machine Learning: Theory and Practice.; 30th Conference on Neural Information Processing Systems (NIPS 2016) ; Conference date: 05-12-2016 Through 10-12-2016",

year = "2016",

month = dec,

language = "الإنجليزيّة",

}

Vaswani, N, Nayer, S & Eldar, YC 2016, 'Non-convex Phase Retrieval of Low-Rank Matrix Columns', Paper presented at 30th Conference on Neural Information Processing Systems (NIPS 2016), Barcelona, Spain, 5/12/16 - 10/12/16. <https://88a73fdb-a-62cb3a1a-s-sites.googlegroups.com/site/nonconvexnips2016/files/Paper11.pdf?attachauth=ANoY7crjtjpG0WScpQYd2fuEGfT6OjMqiOppauF7VxhgV6D2lnIw146xTyy_ffukR9YhIdctUvot507lQkDv_mVj8SjOvCN5GKYO00m0NhYW4y61wezN0wHM1jduidVoxkLgx1j9Ga1DX7v0vYEzQVdPEj7FZ7ty3j2VjvSEj1M8TkW-hR4-4r3cOKcTRFKwkU39DhS2Ssmr6IOSzV98kBSL1AH5EiPPAY6xMeGnEWGplMnsggjV6do%3D&attredirects=0>

TY - CONF

T1 - Non-convex Phase Retrieval of Low-Rank Matrix Columns

AU - Vaswani, Namrata

AU - Nayer, Seyedehsara

AU - Eldar, Yonina C.

N1 - Presented at NIPS 2016 Workshop on Nonconvex Optimization for Machine Learning: Theory and Practice.

PY - 2016/12

Y1 - 2016/12

N2 - We study the problem of recovering a low-rank matrix, X, from phaseless measurements of random linear projections of its columns. In earlier work, we introduced a novel solution approach, called AltMinTrunc, that consisted of a two-step truncated spectral initialization step, followed by a three-step alternating minimization algorithm. In this work, we obtain high probability sample complexity bounds for the AltMinTrunc initialization to provide a good approximation of thetrueX for a specific class of random matrices X. When the rank of X is low enough, these are significantly smaller than what existing single vector phase retrieval algorithms need.

AB - We study the problem of recovering a low-rank matrix, X, from phaseless measurements of random linear projections of its columns. In earlier work, we introduced a novel solution approach, called AltMinTrunc, that consisted of a two-step truncated spectral initialization step, followed by a three-step alternating minimization algorithm. In this work, we obtain high probability sample complexity bounds for the AltMinTrunc initialization to provide a good approximation of thetrueX for a specific class of random matrices X. When the rank of X is low enough, these are significantly smaller than what existing single vector phase retrieval algorithms need.

M3 - محاضرة

T2 - 30th Conference on Neural Information Processing Systems (NIPS 2016)

Y2 - 5 December 2016 through 10 December 2016

ER -

Non-convex Phase Retrieval of Low-Rank Matrix Columns

Abstract

Conference

Access to Document

Fingerprint

Cite this