Diffusion-Inspired Shrinkage Functions and Stability Results for Wavelet Denoising
International Journal of Computer Vision
Channel Smoothing: Efficient Robust Smoothing of Low-Level Signal Features
IEEE Transactions on Pattern Analysis and Machine Intelligence
From two-dimensional nonlinear diffusion to coupled Haar wavelet shrinkage
Journal of Visual Communication and Image Representation
Seismic deconvolution by atomic decomposition: A parametric approach with sparseness constraints
Integrated Computer-Aided Engineering
Engineering Applications of Artificial Intelligence
Correspondences between wavelet shrinkage and nonlinear diffusion
Scale Space'03 Proceedings of the 4th international conference on Scale space methods in computer vision
Review article: Edge and line oriented contour detection: State of the art
Image and Vision Computing
From tensor-driven diffusion to anisotropic wavelet shrinkage
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part I
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Coifman and Donoho (1995) suggested translation-invariant wavelet shrinkage as a way to remove noise from images. Basically, their technique applies wavelet shrinkage to a two-dimensional (2-D) version of the semi-discrete wavelet representation of Mallat and Zhong (1992), Coifman and Donoho also showed how the method could be implemented in O(Nlog N) operations, where there are N pixels. In this paper, we provide a mathematical framework for iterated translation-invariant wavelet shrinkage, and show, using a theorem of Kato and Masuda (1978), that with orthogonal wavelets it is equivalent to gradient descent in L 2(I) along the semi-norm for the Besov space B1 1(L1(I)), which, in turn, can be interpreted as a new nonlinear wavelet-based image smoothing scale space. Unlike many other scale spaces, the characterization is not in terms of a nonlinear partial differential equation