Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Characterization of Signals from Multiscale Edges
IEEE Transactions on Pattern Analysis and Machine Intelligence
Diffusion-Inspired Shrinkage Functions and Stability Results for Wavelet Denoising
International Journal of Computer Vision
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
A new iterated two-band diffusion equation: theory and its application
IEEE Transactions on Image Processing
Image quality assessment: from error visibility to structural similarity
IEEE Transactions on Image Processing
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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.