Discrete Wavelet Diffusion for Image Denoising
Nonlinear diffusion, proposed by Perona-Malik, is a well-known method for image denoising with edge preserving characteristics. Recently, nonlinear diffusion has been shown to be equivalent to iterative wavelet shrinkage, but only for (1) Mallat-Zhong dyadic wavelet transform and (2) Haar wavelet transform. In this paper, we generalize the equivalence of nonlinear diffusion to non-linear shrinkage in the standard discrete wavelet transform (DWT) domain. Two of the major advantages of the standard DWT are its simplicity (as compared to 1) and its potential to benefit from a greater range of orthogonal and biorthogonal filters (as compared to both 1 and 2). We also extend the wavelet diffusion implementation to multiscale. The qualitative and quantitative results shown for a variety of images contaminated with noise demonstrate the promise of the proposed standard wavelet diffusion.
KeywordsDiscrete Wavelet Transform Discrete Wavelet Decomposition Level Nonlinear Diffusion Haar Wavelet
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