Reduction of autoregressive noise with shift-invariant wavelet-packets

We present a new wavelet-based method for reducing additive autoregressive noise. The method uses a shift-invariant wavelet-packet transform to facilitate a linear transformation of wavelet-packet basis vectors. The transformed basis vectors are shown to be better suited than the original basis vectors for use in conventional wavelet-based denoising algorithms which use the minimum description length (MDL) or thresholding approaches. A computational example is presented which demonstrates the advantages of the new algorithm. Autoregressive (AR) models provide a useful tool for adapting the MDL algorithm to the reduction of correlated noise. A straightforward adaptation involves fitting an AR model to the noise component, building an FIR prediction-error filter from the AR model, and using the filter to whiten the noise component.