Abstract
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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