國立虎尾科技大學 |

Accurate Quantization in Redundant Systems : = From Frames to Compressive Sampling and Phase Retrieval.

紀錄類型:	書目-語言資料,手稿 : Monograph/item
正題名/作者:	Accurate Quantization in Redundant Systems :/
其他題名:	From Frames to Compressive Sampling and Phase Retrieval.
作者:	Huynh, Thang.
面頁冊數:	1 online resource (116 pages)
附註:	Source: Dissertation Abstracts International, Volume: 78-05(E), Section: B.
Contained By:	Dissertation Abstracts International78-05B(E).
標題:	Applied mathematics. -
電子資源:	click for full text (PQDT)
ISBN:	9781369331844

Accurate Quantization in Redundant Systems : = From Frames to Compressive Sampling and Phase Retrieval.
Huynh, Thang.

Accurate Quantization in Redundant Systems :From Frames to Compressive Sampling and Phase Retrieval. - 1 online resource (116 pages)

Source: Dissertation Abstracts International, Volume: 78-05(E), Section: B.

Thesis (Ph.D.)

Includes bibliographical references

We study quantization theory and analog-to-digital conversion methods in the settings of frame theory, compressive sampling, and phase retrieval. In the case of frames, we investigate the so-called "Synthesis Problem" of digitally approximating signals by linear combinations of frame vectors with binary coefficients. We obtain exponentially small bounds for the best achievable reconstruction error using random frames. In the setting of compressive sampling, we extend the distributed noise-shaping quantization method of Chou and Gunturk beyond the case of Gaussian measurements to randomly sampled measurements with respect to a bounded orthogonal system including random Fourier measurements. Finally, in the setting of phase retrieval, we apply the same noise shaping method to quantize phaseless measurements and obtain near-optimal recovery guarantees in the case of Gaussian measurements by using a modified version of the PhaseLift algorithm.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2018

Mode of access: World Wide Web

ISBN: 9781369331844Subjects--Topical Terms:

1069907
Applied mathematics.
Index Terms--Genre/Form:

554714
Electronic books.

Accurate Quantization in Redundant Systems : = From Frames to Compressive Sampling and Phase Retrieval.
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245 1 0 $a Accurate Quantization in Redundant Systems : $b From Frames to Compressive Sampling and Phase Retrieval.
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500 $a Source: Dissertation Abstracts International, Volume: 78-05(E), Section: B.
500 $a Adviser: Sinan Gunturk.
502 $a Thesis (Ph.D.) $c New York University $d 2016.
504 $a Includes bibliographical references
520 $a We study quantization theory and analog-to-digital conversion methods in the settings of frame theory, compressive sampling, and phase retrieval. In the case of frames, we investigate the so-called "Synthesis Problem" of digitally approximating signals by linear combinations of frame vectors with binary coefficients. We obtain exponentially small bounds for the best achievable reconstruction error using random frames. In the setting of compressive sampling, we extend the distributed noise-shaping quantization method of Chou and Gunturk beyond the case of Gaussian measurements to randomly sampled measurements with respect to a bounded orthogonal system including random Fourier measurements. Finally, in the setting of phase retrieval, we apply the same noise shaping method to quantize phaseless measurements and obtain near-optimal recovery guarantees in the case of Gaussian measurements by using a modified version of the PhaseLift algorithm.
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
655 7 $a Electronic books. $2 local $3 554714
690 $a 0364
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a New York University. $b Mathematics. $3 1180487
773 0 $t Dissertation Abstracts International $g 78-05B(E).
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