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Ding Y, Xue H, Jin N, et al. The Asymptotic Noise Distribution in Karhunen-Loeve Transform Eigenmodes. J Health Med Inform. 2013;4(2):122doi: 10.4172/2157-7420.1000122.
Ding, Y., Xue, H., Jin, N., Chung, Y. C., Liu, X., Zhang, Y., & Simonetti, O. P. (2013). The Asymptotic Noise Distribution in Karhunen-Loeve Transform Eigenmodes. Journal of health & medical informatics, 4(2), 122. https://doi.org/10.4172/2157-7420.1000122
Ding, Yu, et al. "The Asymptotic Noise Distribution in Karhunen-Loeve Transform Eigenmodes." Journal of health & medical informatics vol. 4,2 (2013): 122. doi: https://doi.org/10.4172/2157-7420.1000122
Ding Y, Xue H, Jin N, Chung YC, Liu X, Zhang Y, Simonetti OP. The Asymptotic Noise Distribution in Karhunen-Loeve Transform Eigenmodes. J Health Med Inform. 2013 Jun;4(2):122. doi: 10.4172/2157-7420.1000122. PMID: 26635997; PMCID: PMC4666531.
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J Health Med Inform. 2013 Jun;4(2):122. doi: 10.4172/2157-7420.1000122.

The Asymptotic Noise Distribution in Karhunen-Loeve Transform Eigenmodes.

Journal of health & medical informatics

Yu Ding, Hui Xue, Ning Jin, Yiu-Cho Chung, Xin Liu, Yongqin Zhang, Orlando P Simonetti

Affiliations

  1. Davis Heart and Lung Research Institute, The Ohio State University, Columbus, USA ; Shenzhen Institute of Advanced Technology of Chinese Academy of Science, Shenzhen, Guangdong, China.
  2. Siemens Corporate Research, Princeton, USA.
  3. Siemens Medical Solutions, Inc., Columbus, USA.
  4. Shenzhen Institute of Advanced Technology of Chinese Academy of Science, Shenzhen, Guangdong, China.
  5. Davis Heart and Lung Research Institute, The Ohio State University, Columbus, USA ; Department of Internal Medicine, The Ohio State University, Columbus, USA ; Department of Biomedical Engineering, The Ohio State University, Columbus, USA ; Department of Radiology, The Ohio State University, Columbus, USA.

PMID: 26635997 PMCID: PMC4666531 DOI: 10.4172/2157-7420.1000122

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

References

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