Image denoising via wavelet-domain spatially adaptive FIR Wiener filtering

Wavelet domain denoising has recently attracted much attention, mostly in conjunction with the coefficient-wise wavelet shrinkage proposed by Donoho (see IEEE Trans. Inform. Theory, vol.41, no.3, p.613-27, May 1995). While shrinkage is asymptotically 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 uncorrelated signal model in the wavelet domain, resulting in scalar (pixel-wise) operations. However, the coefficient clustering often observed in the wavelet domain indicates that coefficients 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 denoising. Using an exponential decay model for autocorrelations, we present a parametric solution for FIR Wiener filtering 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 filter offers impressive denoising performance at modest computational complexity.