Improved wavelet denoising via empirical Wiener filtering

Sandeep P. Ghael; Akbar M. Sayeed; Richard G. Baraniuk

doi:10.1117/12.292799

30 October 1997 Improved wavelet denoising via empirical Wiener filtering

Sandeep P. Ghael, Akbar M. Sayeed, Richard G. Baraniuk

Proceedings Volume 3169, Wavelet Applications in Signal and Image Processing V; (1997) https://doi.org/10.1117/12.292799
Event: Optical Science, Engineering and Instrumentation '97, 1997, San Diego, CA, United States

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 bits for variance or vice versa, the proposed scheme typically decreases both bias and variance compared to wavelet shrinkage.

Citation Download Citation

Sandeep P. Ghael, Akbar M. Sayeed, and Richard G. Baraniuk "Improved wavelet denoising via empirical Wiener filtering", Proc. SPIE 3169, Wavelet Applications in Signal and Image Processing V, (30 October 1997); https://doi.org/10.1117/12.292799

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