Solving Noisy ICA Using Multivariate Wavelet Denoising with an Application to Noisy Latent Variables Regression

A novel approach to solve the independent component analysis (ICA) model in the presence of noise is proposed. We use wavelets as natural denoising tools to solve the noisy ICA model. To do this, we use a multivariate wavelet denoising algorithm allowing spatial and temporal dependency. We propose a...

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Bibliographic Details
Published in:Communications in statistics. Theory and methods 2014-05, Vol.43 (10-12), p.2297-2310
Main Authors: Nassiri, Vahid, Aminghafari, Mina, Mohammad-Djafari, Ali
Format: Article
Language:English
Subjects:
Computer Science
Denoising
Design of experiment
Design of experiments
Economic models
Engineering Sciences
Independent component analysis
Mathematical models
Noise
Noise reduction
Regression
Signal and Image processing
Statistics
Temporal logic
Wavelet
Wavelet transform
Wavelet transforms
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Summary:A novel approach to solve the independent component analysis (ICA) model in the presence of noise is proposed. We use wavelets as natural denoising tools to solve the noisy ICA model. To do this, we use a multivariate wavelet denoising algorithm allowing spatial and temporal dependency. We propose also using a statistical approach, named nested design of experiments, to select the parameters such as wavelet family and thresholding type. This technique helps us to select more convenient combination of the parameters. This approach could be extended to many other problems in which one needs to choose parameters between many choices. The performance of the proposed method is illustrated on the simulated data and promising results are obtained. Also, the suggested method applied in latent variables regression in the presence of noise on real data. The good results confirm the ability of multivariate wavelet denoising to solving noisy ICA.
ISSN:0361-0926
1532-415X
DOI:10.1080/03610926.2013.768662