Survey of image denoising techniques <s> I. Linear Filters <s> We investigate Wiener filtering of wavelet coefficients for signal denoising. Empirically designed wavelet-domain Wiener filters outperform many other denoising algorithms based on wavelet thresholding. However, up to now, it has not been clear how to choose the signal model used to design the filter, because the effect of model selection on the filter performance is difficult to understand. By analyzing the error involved in the Wiener filter designed with an empirically obtained signal model, we show that hard thresholding is typically outperformed by a Wiener filter designed in an alternate wavelet domain. Our analysis furthermore provides a method for selecting the various parameters involved in a wavelet-domain Wiener filtering scheme. <s> BIB001 </s> Survey of image denoising techniques <s> I. Linear Filters <s> 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. <s> BIB002 </s> Survey of image denoising techniques <s> I. Linear Filters <s> In this paper we describe a new method for image denoising. We analyse statistical properties of the wavelet coefficients of natural images. It turns out that there is a strong local covariance structure introduced by the edges. We suggest a model for this covariance which allows us to estimate it from the noisy image. Then Wiener filter is employed in order to remove the noise. <s> BIB003
Linear filters such as Wiener filter in the wavelet domain yield optimal results when the signal corruption can be modeled as a Gaussian process and the accuracy criterion is the mean square error (MSE) BIB003 BIB001 . However, designing a filter based on this assumption frequently results in a filtered image that is more visually displeasing than the original noisy signal, even though the filtering operation successfully reduces the MSE. In BIB002 a wavelet-domain spatiallyadaptive FIR Wiener filtering for image denoising is proposed where wiener filtering is performed only within each scale and intrascale filtering is not allowed. 