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

Author

Listed:
  • Vahid Nassiri
  • Mina Aminghafari
  • Ali Mohammad-Djafari

Abstract

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.

Suggested Citation

  • Vahid Nassiri & Mina Aminghafari & Ali Mohammad-Djafari, 2014. "Solving Noisy ICA Using Multivariate Wavelet Denoising with an Application to Noisy Latent Variables Regression," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 43(10-12), pages 2297-2310, May.
    • Handle: RePEc:taf:lstaxx:v:43:y:2014:i:10-12:p:2297-2310
    DOI: 10.1080/03610926.2013.768662
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