In this paper, we propose novel adaptive wavelet filter bank structures based on the lifting scheme. The filter banks are nonseparable, based on quincunx sampling, with their properties being pixel-wise adapted according to the local image features. Despite being adaptive, the filter banks retain a desirable number of primal and dual vanishing moments. The adaptation is introduced in the predict stage of the filter bank with an adaptation region chosen independently for each pixel, based on the intersection of confidence intervals (ICI) rule. The image denoising results are presented for both synthetic and real-world images. It is shown that the obtained wavelet decompositions perform well, especially for synthetic images that contain periodic patterns, for which the proposed method outperforms the state of the art in image denoising.

In this letter, we have proposed a signal denoising method based on a modification of the intersection of confidence intervals (ICI) rule. The ICI rule is complemented by the relative intersection of confidence intervals length which is used as an additional criterion for adaptive filter support selection. It is shown that the proposed method outperforms the original ICI method equipped with the local polynomial approximation (LPA), as well as various conventional wavelet shrinkage methods.

In this paper, we explore the use of nonseparable and adaptive wavelet decompositions for the purpose of image denoising. We apply the classical wavelet shrinkage methods on the wavelet coefficients obtained by using the adaptive wavelet transform defined on the quincunx grid. The wavelet transform is pixel-wise adaptive in all decomposition levels. While providing more compact representation of the analyzed image, the adaptive transform retains some useful properties of fixed transforms, such as numbers of vanishing moments of primal and dual wavelets. The adaptive wavelet decomposition is realized using the lifting scheme. For comparison purposes, the image denoising results are presented for both fixed and adaptive wavelet transforms.