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Tensor completion for multidimension...
~
Hafftka, Ariel.
Tensor completion for multidimensional inverse problems with applications to magnetic resonance relaxometry.
紀錄類型:
書目-語言資料,手稿 : Monograph/item
正題名/作者:
Tensor completion for multidimensional inverse problems with applications to magnetic resonance relaxometry./
作者:
Hafftka, Ariel.
面頁冊數:
1 online resource (171 pages)
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:
click for full text (PQDT)
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.
- 1 online resource (171 pages)
Source: Dissertation Abstracts International, Volume: 77-10(E), Section: B.
Thesis (Ph.D.)
Includes bibliographical references
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.
Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2018
Mode of access: World Wide Web
ISBN: 9781339866512Subjects--Topical Terms:
1069907
Applied mathematics.
Index Terms--Genre/Form:
554714
Electronic books.
Tensor completion for multidimensional inverse problems with applications to magnetic resonance relaxometry.
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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.
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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.
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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.
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