Adaptive Wiener denoising using a Gaussian scale mixture model in the wavelet domain

Image denoising based on the edge-process model

“…A more complex form of the Wiener filter (4) should be used, but this would not be attractive for many practical applications. Moreover, without this correlation assumption this algorithm [22] provides poorer quality (in terms of the PSNR) of the denoised image than the technique proposed in this paper. In order to complete experimental validation of the developed algorithms, denoising results obtained using these techniques versus those one presented in [17] and [22] are given in Figures 10 and 11 for visual quality comparison.…”

“…Due to the fact that none of the candidates is simultaneously the best for the case of two test images, the benchmarking was performed using the average PSNR for these images for a particular noise variance value ( Table 1). The average PSNR results prove that for the critically sampled transform the performance of the proposed algorithm is the best among known Bayesian techniques, but for the case of the overcomplete domain the method proposed in [22] provides better results. The first explanation for this comes from the low robustness to noise of the segmentation, which leads to a bias during the partitioning process.…”

“…In this case, a processing applied to denoise the image operates with covariance matrices rather than exploits correspondent local variances. Experimental results presented in [22] show that this method provides the best quality of the…”

“…A denoising technique that exploits an improved version of the EQ model and this type of transformation demonstrated a very good performance [21]. The recent work of Sterla et al [22] presented a more powerful transform with a larger amount of spatial orientations (steerable pyramid [23]) that could bring additional benefit for the performance of the algorithm. But the main advantage is coming from the correct assumption made about the image statistics or about the stochastic model of the data that are supposed to be correlated in the transform domain.…”

“…But the main advantage is coming from the correct assumption made about the image statistics or about the stochastic model of the data that are supposed to be correlated in the transform domain. The data in this transform domain is caracterized by a Gaussian mixture model [22], where a random vector a can be expressed as the following product: a d = b √ c of a zero-mean Gaussian vector b and an independent positive scalar √ c and equality is with respect to the correspondent pdfs. In this case, a processing applied to denoise the image operates with covariance matrices rather than exploits correspondent local variances.…”