Wavelet Filtering of Speckle Noise - Some Numerical Results

Abstract

We present our most recent results about an ongoing study addressing the comparison of various speckle reduc-tion filters. In a previous work, we have concentrated on the best Signal-to-Mean-Square-Error (S/MSE) ratio provided by a complex Wavelet Coefficient Shrinkage (WCS) filter and several standard speckle filters. Here we specifically address the numerical behavior of the WCS filter over a change (1) in the regularity and type of the wavelet (orthogonal versus bi-orthogonal) and (2) in the wavelet coefficient threshold-ing type (soft- versus hard-thresholding). We also present measures of the variation of the S/MSE over a wide range of the WCS filter parameters in order to provide information on the optimal application range of the filter in practical sit-uations. As in our previous work, tests are performed on optical imagery with a simulated multiplicative Log-Normal noise. The S/MSE ratio is measured after averaging the fil-tered images over 16 diagonal shifts of the Discrete Wavelet Transform (DWT) in order to approximate a shift invariant DWT. Our experiments show, among other, that the optimal threshold level depends on the spectral content of the image and that the soft-thresholding scheme is the best choice for images with high spectral content. 1