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Tensor completion for multidimension...

Hafftka, Ariel.

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Tensor completion for multidimensional inverse problems with applications to magnetic resonance relaxometry.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Tensor completion for multidimensional inverse problems with applications to magnetic resonance relaxometry./
作者:	Hafftka, Ariel.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 2016,
面頁冊數:	171 p.
附註:	Source: Dissertation Abstracts International, Volume: 77-10(E), Section: B.
Contained By:	Dissertation Abstracts International77-10B(E).
標題:	Applied mathematics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10128650
ISBN:	9781339866512

Tensor completion for multidimensional inverse problems with applications to magnetic resonance relaxometry.
Hafftka, Ariel.

Tensor completion for multidimensional inverse problems with applications to magnetic resonance relaxometry. - Ann Arbor : ProQuest Dissertations & Theses, 2016 - 171 p.

Source: Dissertation Abstracts International, Volume: 77-10(E), Section: B.

Thesis (Ph.D.)--University of Maryland, College Park, 2016.

This thesis deals with tensor completion for the solution of multidimensional inverse problems. We study the problem of reconstructing an approximately low rank tensor from a small number of noisy linear measurements. New recovery guarantees, numerical algorithms, non-uniform sampling strategies, and parameter selection algorithms are developed.

ISBN: 9781339866512Subjects--Topical Terms:

2122814
Applied mathematics.

Tensor completion for multidimensional inverse problems with applications to magnetic resonance relaxometry.
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300 $a 171 p.
500 $a Source: Dissertation Abstracts International, Volume: 77-10(E), Section: B.
500 $a Adviser: Wojciech Czaja.
502 $a Thesis (Ph.D.)--University of Maryland, College Park, 2016.
520 $a This thesis deals with tensor completion for the solution of multidimensional inverse problems. We study the problem of reconstructing an approximately low rank tensor from a small number of noisy linear measurements. New recovery guarantees, numerical algorithms, non-uniform sampling strategies, and parameter selection algorithms are developed.
520 $a We derive a fixed point continuation algorithm for tensor completion and prove its convergence. A restricted isometry property (RIP) based tensor recovery guarantee is proved. Probabilistic recovery guarantees are obtained for sub-Gaussian measurement operators and for measurements obtained by non-uniform sampling from a Parseval tight frame.
520 $a We show how tensor completion can be used to solve multidimensional inverse problems arising in NMR relaxometry. Algorithms are developed for regularization parameter selection, including accelerated k-fold cross-validation and generalized cross-validation. These methods are validated on experimental and simulated data. We also derive condition number estimates for nonnegative least squares problems.
520 $a Tensor recovery promises to significantly accelerate N-dimensional NMR relaxometry and related experiments, enabling previously impractical experiments. Our methods could also be applied to other inverse problems arising in machine learning, image processing, signal processing, computer vision, and other fields.
590 $a School code: 0117.
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