|
Title:
|
Improved Wavelet Denoising via Empirical Wiener Filtering |
|
Author:
|
Ghael, Sadeep; Sayeed, Akbar M.; Baraniuk, Richard G.
|
|
Type:
|
Conference Paper |
|
Keywords:
|
wavelets; denoising; estimation; Wiener filter; subspace |
|
Citation:
|
S. Ghael, A. M. Sayeed and R. G. Baraniuk,"Improved Wavelet Denoising via Empirical Wiener Filtering," in SPIE Technical Conference on Wavelet Applications in Signal Processing, |
|
Abstract:
|
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. |
|
Date Published:
|
1997-07-01 |
