Image Denoising via Wavelet - Domain

Wavelet domain denoising has recently attracted much attention , mostly in conjunction with the coeecient-wise wavelet shrinkage proposed by Donoho 1]. While shrinkage is asymp-totically minimax-optimal, in many image processing applications a mean-squares solution is preferable. Most MMSE solutions that have appeared so far are based on an un-correlated signal model in the wavelet domain, resulting in scalar (pixel-wise) operations. However, the coeecient clustering often observed in the wavelet domain indicates that coeecients are not independent. Especially in the case of undecimated discrete wavelet transform (UDWT), both the signal and noise components are non-white, thus motivating a more powerful model. This paper proposes a simple yet powerful extension to the pixel-wise MMSE wavelet denois-ing. Using an exponential decay model for autocorrelations, we present a parametric solution for FIR Wiener ltering in the wavelet domain. This solution takes into account the colored nature of signal and noise in UDWT, and is adaptively trained via a simple context model. The resulting Wiener lter ooers impressive denoising performance at modest computational complexity.