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ISSN: 2157-7420

Journal of Health & Medical Informatics
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  • Research Article   
  • J Health Med Inform 2013, Vol 4(2)
  • DOI: 10.4172/2157-7420.1000122

The Asymptotic Noise Distribution in Karhunen-Loeve Transform Eigenmodes

Yu Ding1,2, Hui Xue3*, Ning Jin4, Yiu-Cho Chung2, Xin Liu2, Yongqin Zhang2 and Orlando P. Simonetti1,5,6,7
1Davis Heart and Lung Research Institute, The Ohio State University, Columbus, USA
2Shenzhen Institute of Advanced Technology of Chinese Academy of Science, , Shenzhen, Guangdong, China
3Siemens Corporate Research, , Princeton, USA
4Siemens Medical Solutions, Inc., , Columbus, USA
5Department of Internal Medicine, The Ohio State University, Columbus, USA
6Department of Biomedical Engineering, The Ohio State University, Columbus, USA
7Department of Radiology, The Ohio State University, Columbus, USA
*Corresponding Author : Hui Xue, Siemens Corporation, Corporate Research, 755 College Road East, Princeton, NJ 08540, USA, Tel: +1(609)734-6560, +1(609)712-3398, Fax: +1(609)734-6565, Email: [email protected]

Received Date: Dec 01, 2012 / Accepted Date: Feb 01, 2013 / Published Date: Feb 03, 2013

Abstract

 Karhunen-Loeve Transform (KLT) is widely used in signal processing. Yet the well-accepted result is that, the noise

is uniformly distributed in all eigenmodes is not accurate. We apply a result of the random matrix theory to understand
the asymptotic noise distribution in KLT eigenmodes. Noise variances in noise-only eigenmodes follow the Marcenko-
Pastur distribution, while noise variances in signal-dominated eigenmodes still follow the uniform distribution. Both the
mathematical expectation of noise level in each eigenmode and an analytical formula of KLT filter noise reduction effect
with a hard threshold were derived. Numerical simulations agree with our theoretical analysis. The noise variance of
an eigenmode may deviate more than 60% from the uniform distribution. These results can be modified slightly, and
generalized to non-IID (independently and identically-distributed) noise scenario. Magnetic resonance imaging experiments
show that the generalized result is applicable and accurate. These generic results can help us understand the
noise behavior in the KLT and related topics.

Keywords: Karhunen-Loeve transform; Random matrix theory; Independently and identically-distributed noise

Citation: Ding Y, Xue H, Jin N, Chung YC, Liu X, et al. (2013) The Asymptotic Noise Distribution in Karhunen-Loeve Transform Eigenmodes. J Health Med Inform 4:122. Doi: 10.4172/2157-7420.1000122

Copyright: © 2013 Ding Y, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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