國立虎尾科技大學 |

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

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Tensor completion for multidimensional inverse problems with applications to magnetic resonance relaxometry./
Author:	Hafftka, Ariel.
Description:	1 online resource (171 pages)
Notes:	Source: Dissertation Abstracts International, Volume: 77-10(E), Section: B.
Contained By:	Dissertation Abstracts International77-10B(E).
Subject:	Applied mathematics. -
Online resource:	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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035 $a AAI10128650
040 $a MiAaPQ $b eng $c MiAaPQ
099 $a TUL $f hyy $c available through World Wide Web
100 1 $a Hafftka, Ariel. $3 1180466
245 1 0 $a Tensor completion for multidimensional inverse problems with applications to magnetic resonance relaxometry.
264 0 $c 2016
300 $a 1 online resource (171 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
500 $a Source: Dissertation Abstracts International, Volume: 77-10(E), Section: B.
500 $a Adviser: Wojciech Czaja.
502 $a Thesis (Ph.D.) $c University of Maryland, College Park $d 2016.
504 $a Includes bibliographical references
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.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2018
538 $a Mode of access: World Wide Web
650 4 $a Applied mathematics. $3 1069907
650 4 $a Mathematics. $3 527692
650 4 $a Medical imaging. $3 1180167
655 7 $a Electronic books. $2 local $3 554714
690 $a 0364
690 $a 0405
690 $a 0574
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a University of Maryland, College Park. $b Applied Mathematics and Scientific Computation. $3 1180467
773 0 $t Dissertation Abstracts International $g 77-10B(E).
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10128650 $z click for full text (PQDT)