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High Dimensional Signal Representation.
~
ProQuest Information and Learning Co.
High Dimensional Signal Representation.
Record Type:
Language materials, manuscript : Monograph/item
Title/Author:
High Dimensional Signal Representation./
Author:
Yin, Rujie.
Description:
1 online resource (185 pages)
Notes:
Source: Dissertation Abstracts International, Volume: 78-09(E), Section: B.
Contained By:
Dissertation Abstracts International78-09B(E).
Subject:
Mathematics. -
Online resource:
click for full text (PQDT)
ISBN:
9781369719703
High Dimensional Signal Representation.
Yin, Rujie.
High Dimensional Signal Representation.
- 1 online resource (185 pages)
Source: Dissertation Abstracts International, Volume: 78-09(E), Section: B.
Thesis (Ph.D.)
Includes bibliographical references
In this thesis we explore the efficiency of signal representations and their robustness in signal reconstruction in three subfields of signal and image processing.
Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2018
Mode of access: World Wide Web
ISBN: 9781369719703Subjects--Topical Terms:
527692
Mathematics.
Index Terms--Genre/Form:
554714
Electronic books.
High Dimensional Signal Representation.
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High Dimensional Signal Representation.
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2017
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1 online resource (185 pages)
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Source: Dissertation Abstracts International, Volume: 78-09(E), Section: B.
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Adviser: Ingrid Daubechies.
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Thesis (Ph.D.)
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Duke University
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2017.
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Includes bibliographical references
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In this thesis we explore the efficiency of signal representations and their robustness in signal reconstruction in three subfields of signal and image processing.
520
$a
The first result concerns regularity limitation in the construction of directional wavelet bases due to redundancy constraint on the scheme, in an effort to construct "optimal" directional bases with multiresolution and perfect reconstruction properties. We showed that for orthonormal and biorthogonal bases with dilated quincunx downsampling, the wavelets cannot be well localized; however, this regularity limit can be circumvented in a tight frame with dyadic downsampling and a redundancy factor smaller than 2.
520
$a
The second result introduces a novel framework for patch-based image models combining local structure of patches and nonlocal information in image domain. In particular, we built convolution framelets from local and nonlocal bases, which form a tight frame of the image space and has energy concentration when the local and nonlocal bases are coherent. We applied this framework to reinterpret and improve state-of-the-art low dimensional manifold model.
520
$a
The final result proposes a new paradigm of phase retrieval, considering signal reconstruction up to a larger equivalence class than a uniform phase shift. It is known that in the classical setting, phase retrieval in infinite or high dimension is inherently unstable. We showed that stability can be achieved, however, for frames of Gabor wavelets or Cauchy wavelets in this new paradigm.
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Ann Arbor, Mich. :
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ProQuest,
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2018
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Mode of access: World Wide Web
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Mathematics.
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554714
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ProQuest Information and Learning Co.
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Duke University.
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http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10257614
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click for full text (PQDT)
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