TO IEEE TRANSACTIONS ON IMAGE PROCESSING 1 Wavelet Thresholding for Multiple

This work addresses the recovery of an image from its multiple noisy copies. The standard method is to compute the weighted average of these copies. Since the wavelet thresholding technique has been shown to eeectively denoise a single noisy copy, we consider in this paper combining the two operations of averaging and thresholding. Because thresholding is a non-linear technique, averaging then thresholding or thresholding then averaging produce diierent estimators. By modeling the signal wavelet coeecients as Laplacian distributed and the noise as Gaussian, our investigation nds the optimal ordering to depend on the number of available copies and on the signal-to-noise ratio. We then propose thresholds that are nearly optimal under the assumed model for each ordering. With the optimal and near-optimal thresholds, the two methods yield similar performance, and both show considerable improvement over merely averaging.