ERA

Download the full-sized PDF of The Strong Restricted Isometry Property of Sub-Gaussian Matrices and the Erasure Robustness Property of Gaussian Random FramesDownload the full-sized PDF

Analytics

Share

Permanent link (DOI): https://doi.org/10.7939/R3JD4Q09H

Download

Export to: EndNote  |  Zotero  |  Mendeley

Communities

This file is in the following communities:

Graduate Studies and Research, Faculty of

Collections

This file is in the following collections:

Theses and Dissertations

The Strong Restricted Isometry Property of Sub-Gaussian Matrices and the Erasure Robustness Property of Gaussian Random Frames Open Access

Descriptions

Other title
Subject/Keyword
restricted isometry property
random matrix
compressed sensing
Type of item
Thesis
Degree grantor
University of Alberta
Author or creator
Lu, Ran
Supervisor and department
Wong, Yau S (Mathematical and Statistical Sciences)
Han, Bin (Mathematical and Statistical Sciences)
Examining committee member and department
Wong, Yau Shu (Mathematical and Statistical Sciences)
Han, Bin (Mathematical and Statistical Sciences)
Dai, Feng (Mathematical and Statistical Sciences)
Alexander Litvak (Mathematical and Statistical Sciences)
Lau, Anthony T-M (Mathematical and Statistical Sciences)
Department
Department of Mathematical and Statistical Sciences
Specialization
Applied Mathematics
Date accepted
2016-03-30T10:13:04Z
Graduation date
2016-06
Degree
Master of Science
Degree level
Master's
Abstract
In this thesis we will study the robustness property of sub-gaussian random matrices. We first show that the nearly isometry property will still hold with high probability if we erase a certain portion of rows from a sub-gaussian matrix, and we will estimate the erasure ratio with a given small distortion rate in the norm. With this, we establish the strong restricted isometry property (SRIP) and the robust version of Johnson-Lindenstrauss (JL) Lemma for sub-gaussian matrices, which are essential in compressed sensing with corruptions. Then we fix the erasure ratio and deduce the lower and upper bounds of the norm after a erased sub-gaussian matrix acting on a vector, and in this case we can also obtain the corresponding SRIP and the robust version of JL Lemma. Finally, we study the robustness property of Gaussian random finite frames, we will improve existing results.
Language
English
DOI
doi:10.7939/R3JD4Q09H
Rights
This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for the purpose of private, scholarly or scientific research. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.
Citation for previous publication

File Details

Date Uploaded
Date Modified
2016-03-30T16:13:13.536+00:00
Audit Status
Audits have not yet been run on this file.
Characterization
File format: pdf (Portable Document Format)
Mime type: application/pdf
File size: 458248
Last modified: 2016:06:16 16:53:33-06:00
Filename: Lu_Ran_201603_MSc.pdf
Original checksum: 112af4a1948da73c0888b7163cecdfce
Well formed: true
Valid: true
File title: Introduction
Page count: 86
Activity of users you follow
User Activity Date