Approximating the Best Linear Unbiased Estimator of Non-Gaussian Signals with Gaussian Noise

Masashi SUGIYAMA  Motoaki KAWANABE  Gilles BLANCHARD  Klaus-Robert MULLER  

IEICE TRANSACTIONS on Information and Systems   Vol.E91-D   No.5   pp.1577-1580
Publication Date: 2008/05/01
Online ISSN: 1745-1361
DOI: 10.1093/ietisy/e91-d.5.1577
Print ISSN: 0916-8532
Type of Manuscript: LETTER
Category: Pattern Recognition
signal denoising,  best linear unbiased estimator (BLUE),  non-Gaussian component analysis (NGCA),  Gaussian noise,  

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Obtaining the best linear unbiased estimator (BLUE) of noisy signals is a traditional but powerful approach to noise reduction. Explicitly computing the BLUE usually requires the prior knowledge of the noise covariance matrix and the subspace to which the true signal belongs. However, such prior knowledge is often unavailable in reality, which prevents us from applying the BLUE to real-world problems. To cope with this problem, we give a practical procedure for approximating the BLUE without such prior knowledge. Our additional assumption is that the true signal follows a non-Gaussian distribution while the noise is Gaussian.