Adaptation in the Quincunx Wavelet Filter Bank with Applications in Image Denoising

In this paper, we present the realization of an adaptive shift invariant wavelet transform defined on the quincunx grid. The wavelet transform relies on the lifting scheme which enables us to easily introduce the adaptation by splitting the predict stage into two parts. The first part of the predict stage is fixed and guarantees the number of vanishing moments of the wavelet filter bank while the second part can adapt to the local properties of the analyzed image. In this paper, we explore the robustness of the generalized least squares adaptation algorithm to the noise present in the analyzed image. The denoising results obtained with the nonseparable adaptive wavelet transform have been compared with results obtained with both separable and nonseparable fixed wavelet transforms. Also, the empirical Wiener filtering in the wavelet domain has been used in order to further improve the denoising results.