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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.