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The Asymptotic Noise Distribution in Karhunen-Loeve Transform Eigenmodes
1Davis Heart and Lung Research Institute, The Ohio State University, Columbus, USA ; Shenzhen Institute of Advanced Technology of Chinese Academy of Science, Shenzhen, Guangdong, China.
Journal of Health & Medical Informatics
|December 5, 2015
Summary
Noise distribution in Karhunen-Loeve Transform (KLT) eigenmodes is not uniform. Random matrix theory reveals noise variances in noise-only modes follow Marcenko-Pastur, aiding KLT filter analysis.
Area of Science:
- Signal Processing
- Random Matrix Theory
- Statistical Analysis
Background:
- Karhunen-Loeve Transform (KLT) is a standard technique in signal processing.
- The assumption of uniform noise distribution across KLT eigenmodes is prevalent but inaccurate.
Purpose of the Study:
- To investigate the asymptotic noise distribution in KLT eigenmodes using random matrix theory.
- To derive analytical formulas for noise levels and KLT filter performance.
Main Methods:
- Application of random matrix theory to analyze noise distribution in KLT.
- Derivation of mathematical expectations for noise levels in eigenmodes.
- Development of an analytical formula for KLT filter noise reduction with hard thresholding.
Main Results:
- Noise variances in noise-only eigenmodes conform to the Marcenko-Pastur distribution.
- Noise variances in signal-dominated eigenmodes remain uniformly distributed.
- Theoretical analysis confirmed by numerical simulations, showing potential deviations over 60% from uniform distribution.
Conclusions:
- The study provides a more accurate model for noise distribution in KLT eigenmodes.
- Derived formulas offer insights into KLT filter noise reduction efficacy.
- Generalization to non-IID noise scenarios validated by Magnetic Resonance Imaging experiments.
Keywords:
Independently and identically-distributed noiseKarhunen-Loeve transformRandom matrix theoryMore Related Videos
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