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Sampling and Filtering of Signals on...

Gadde, Akshay.

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Sampling and Filtering of Signals on Graphs With Applications to Active Learning and Image Processing.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Sampling and Filtering of Signals on Graphs With Applications to Active Learning and Image Processing./
Author:	Gadde, Akshay.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2017,
Description:	112 p.
Notes:	Source: Dissertation Abstracts International, Volume: 79-06(E), Section: B.
Contained By:	Dissertation Abstracts International79-06B(E).
Subject:	Electrical engineering. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10820624

Sampling and Filtering of Signals on Graphs With Applications to Active Learning and Image Processing.
Gadde, Akshay.

Sampling and Filtering of Signals on Graphs With Applications to Active Learning and Image Processing. - Ann Arbor : ProQuest Dissertations & Theses, 2017 - 112 p.

Source: Dissertation Abstracts International, Volume: 79-06(E), Section: B.

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

Graph signals provide a natural representation for data in many applications such as social networks, web information analysis, sensor networks and machine learning. Traditional data such as images and videos can also be represented as signals on graphs. A frequency domain representation for graph signals can be obtained using the eigenvectors and eigenvalues of operators that measure the variation in signals taking into account the underlying connectivity in the graph. Based on this, we develop a sampling theory for graph signals that answers the following questions: 1. When can we uniquely and stably reconstruct a bandlimited graph signal from its samples on a subset of the nodes? 2. What is the best subset of nodes for sampling a signal so that the resulting bandlimited reconstruction is most stable? 3. How to compute a bandlimited reconstruction efficiently from a subset of samples? The algorithms developed for sampling set selection and reconstruction do not require explicit eigenvalue decomposition of the variation operator and admit efficient, localized implementation. Using graph sampling theory, we propose effective graph based active semi-supervised learning techniques. We also give a probabilistic interpretation of graph sampling. Based on this interpretation, we generalize the framework of sampling on graphs using Bayesian methods to give an adaptive sampling method in which the future choice of nodes to be sampled depends on the samples observed in the past. Additionally, we study the problem of constructing a sparse graph efficiently from given data and a kernel function that measures pairwise similarity between data points. The proposed graph construction method leads to graph based learning and clustering algorithms that outperform the conventional k-nearest neighbor methods. We also use the proposed graph construction method to provide an efficient alternative to the well-known bilateral filter by representing an image as a sparse graph in which the nodes correspond to the pixels in the image.Subjects--Topical Terms:

649834
Electrical engineering.

Sampling and Filtering of Signals on Graphs With Applications to Active Learning and Image Processing.
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245 1 0 $a Sampling and Filtering of Signals on Graphs With Applications to Active Learning and Image Processing.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2017
300 $a 112 p.
500 $a Source: Dissertation Abstracts International, Volume: 79-06(E), Section: B.
500 $a Adviser: Antonio Ortega.
502 $a Thesis (Ph.D.)--University of Southern California, 2017.
520 $a Graph signals provide a natural representation for data in many applications such as social networks, web information analysis, sensor networks and machine learning. Traditional data such as images and videos can also be represented as signals on graphs. A frequency domain representation for graph signals can be obtained using the eigenvectors and eigenvalues of operators that measure the variation in signals taking into account the underlying connectivity in the graph. Based on this, we develop a sampling theory for graph signals that answers the following questions: 1. When can we uniquely and stably reconstruct a bandlimited graph signal from its samples on a subset of the nodes? 2. What is the best subset of nodes for sampling a signal so that the resulting bandlimited reconstruction is most stable? 3. How to compute a bandlimited reconstruction efficiently from a subset of samples? The algorithms developed for sampling set selection and reconstruction do not require explicit eigenvalue decomposition of the variation operator and admit efficient, localized implementation. Using graph sampling theory, we propose effective graph based active semi-supervised learning techniques. We also give a probabilistic interpretation of graph sampling. Based on this interpretation, we generalize the framework of sampling on graphs using Bayesian methods to give an adaptive sampling method in which the future choice of nodes to be sampled depends on the samples observed in the past. Additionally, we study the problem of constructing a sparse graph efficiently from given data and a kernel function that measures pairwise similarity between data points. The proposed graph construction method leads to graph based learning and clustering algorithms that outperform the conventional k-nearest neighbor methods. We also use the proposed graph construction method to provide an efficient alternative to the well-known bilateral filter by representing an image as a sparse graph in which the nodes correspond to the pixels in the image.
590 $a School code: 0208.
650 4 $a Electrical engineering. $3 649834
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710 2 $a University of Southern California. $3 700129
773 0 $t Dissertation Abstracts International $g 79-06B(E).
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791 $a Ph.D.
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793 $a English
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