東華大學圖書館 |

Language: English

Help

回圖書館首頁

手機版館藏查詢

Back

Switch To: Labeled | MARC Mode | ISBD

Nonlocal Variational Methods in Imag...

Zhu, Wei.

Linked to FindBook

Google Book

Amazon

博客來

Nonlocal Variational Methods in Image and Data Processing.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Nonlocal Variational Methods in Image and Data Processing./
Author:	Zhu, Wei.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2017,
Description:	136 p.
Notes:	Source: Dissertation Abstracts International, Volume: 78-10(E), Section: B.
Contained By:	Dissertation Abstracts International78-10B(E).
Subject:	Applied mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10285520
ISBN:	9781369827262

Nonlocal Variational Methods in Image and Data Processing.
Zhu, Wei.

Nonlocal Variational Methods in Image and Data Processing. - Ann Arbor : ProQuest Dissertations & Theses, 2017 - 136 p.

Source: Dissertation Abstracts International, Volume: 78-10(E), Section: B.

Thesis (Ph.D.)--University of California, Los Angeles, 2017.

In this dissertation, two nonlocal variational models for image and data processing are presented: nonlocal total variation (NLTV) for unsupervised hyperspectral image classification, and low dimensional manifold model (LDMM) for general image and data processing problems. Both models utilize the nonlocal patch-based structures in natural images and data, and modern optimization techniques are used to solve the corresponding variational problems. The proposed algorithms achieve state-of-the-art results on various image and data processing problems, in particular unsupervised hyperspectral image classification and image or data interpolation.

ISBN: 9781369827262Subjects--Topical Terms:

2122814
Applied mathematics.

Nonlocal Variational Methods in Image and Data Processing.
LDR:04022nmm a2200313 4500 001 2122711
005 20170922124940.5
008 180830s2017 ||||||||||||||||| ||eng d
020 $a 9781369827262
035 $a (MiAaPQ)AAI10285520
035 $a AAI10285520
040 $a MiAaPQ $c MiAaPQ
100 1 $a Zhu, Wei. $3 1928594
245 1 0 $a Nonlocal Variational Methods in Image and Data Processing.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2017
300 $a 136 p.
500 $a Source: Dissertation Abstracts International, Volume: 78-10(E), Section: B.
500 $a Adviser: Stanley J. Osher.
502 $a Thesis (Ph.D.)--University of California, Los Angeles, 2017.
520 $a In this dissertation, two nonlocal variational models for image and data processing are presented: nonlocal total variation (NLTV) for unsupervised hyperspectral image classification, and low dimensional manifold model (LDMM) for general image and data processing problems. Both models utilize the nonlocal patch-based structures in natural images and data, and modern optimization techniques are used to solve the corresponding variational problems. The proposed algorithms achieve state-of-the-art results on various image and data processing problems, in particular unsupervised hyperspectral image classification and image or data interpolation.
520 $a First, a graph-based nonlocal total variation method is proposed for unsupervised classification of hyperspectral images (HSI). The variational problem is solved by the primal-dual hybrid gradient (PDHG) algorithm. By squaring the labeling function and using a stable simplex clustering routine, an unsupervised clustering method with random initialization can be implemented. The effectiveness of the proposed algorithm is illustrated on both synthetic and real-world HSI, and numerical results show that the proposed algorithm outperforms other standard unsupervised clustering methods such as spherical K-means, nonnegative matrix factorization (NMF), and the graph-based Merriman-Bence-Osher (MBO) scheme.
520 $a Next, we present a novel low dimensional manifold model for general image processing problems. LDMM is based on the fact that the patch manifolds of many natural images have low dimensional structures. Based on this observation, the dimension of the patch manifold is used as a regularization to recover the image. The key step in LDMM is to solve a Laplace-Beltrami equation over a point cloud, and it is tackled by the point integral method (PIM). The point integral method enforces the sample point constraints correctly and yields better results than the standard graph Laplacian. LDMM can be used for various image processing problems, and it achieves state-of-the-art results for image inpainting from random subsampling.
520 $a Lastly, we present an alternative way to solve the Laplace-Beltrami equation in LDMM. Although the point integral method correctly enforces the sample point constraints and achieves excellent results for image inpainting, the resulting linear system is on the patch domain, and hundreds of linear systems need to be solved each iteration. This causes LDMM to be computationally infeasible for large images and high dimensional data. An alternative way is to discretize the Laplace-Beltrami operator with the weighted graph Laplacian (WGL). After such discretization, we only need to solve one symmetric sparse linear system per iteration of manifold update for image inpainting. Moreover, semi-local patches that in- corporate coordinate information of the patches are used in the weight update, which leads to a faster convergence of LDMM. Numerical experiments on normal image, hyperspectral image, and high dimensional scientific data interpolation demonstrate the effectiveness of the algorithm.
590 $a School code: 0031.
650 4 $a Applied mathematics. $3 2122814
690 $a 0364
710 2 $a University of California, Los Angeles. $b Mathematics 0540. $3 2096468
773 0 $t Dissertation Abstracts International $g 78-10B(E).
790 $a 0031
791 $a Ph.D.
792 $a 2017
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10285520