Improved Wavelet Denoising via Empirical Wiener Filtering

S. Ghael, A. M. Sayeed, and R. G. Baraniuk

Department of Electrical and Computer Engineering
Rice University
Houston, TX  77005-1892
Email:   richb@rice.edu


  Wavelet shrinkage is a signal estimation technique that exploits the
  remarkable abilities of the wavelet transform for signal
  compression.  Wavelet shrinkage using thresholding is asymptotically
  optimal in a minimax mean-square error (MSE) sense over a variety of
  smoothness spaces. However, for any given signal, the MSE-optimal
  processing is achieved by the Wiener filter, which delivers
  substantially improved performance.

  In this paper, we develop a new algorithm for wavelet denoising that
  uses a wavelet shrinkage estimate as a means to design a
  wavelet-domain Wiener filter. The shrinkage estimate indirectly
  yields an estimate of the signal subspace that is leveraged into the
  design of the filter.  A peculiar aspect of the algorithm is its use
  of two wavelet bases: one for the design of the empirical Wiener
  filter and one for its application. Simulation results show up to a
  factor of 2 improvement in MSE over wavelet shrinkage, with a
  corresponding improvement in visual quality of the estimate.
  Simulations also yield a remarkable observation: whereas shrinkage
  estimates typically improve performance by trading bias for variance
  or vice versa, the proposed scheme typically decreases both bias and
  variance compared to wavelet shrinkage.