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Reduction of correlated noise using a library of orthonormal bases

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1 Author(s)
Villemoes, L.F. ; Dept. of Math., R. Inst. of Technol., Stockholm, Sweden

We study the application of a library of orthonormal bases to the reduction of correlated Gaussian noise. A joint condition on the library and the noise covariance is derived which ensures that simple thresholding in an adaptively chosen basis yields an estimation error within a logarithmic factor of the ideal risk. In the model example of a wavelet packet library and stationary noise the condition can be translated into a reverse Holder inequality on the power spectrum

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Information Theory, IEEE Transactions on  (Volume:48 ,  Issue: 2 )