Ten lectures on wavelets
Choice of wavelet smoothness, primary resolution and threshold in wavelet shrinkage
Statistics and Computing
Bivariate shrinkage functions for wavelet-based denoising exploiting interscale dependency
IEEE Transactions on Signal Processing
A Nonlinear Stein-Based Estimator for Multichannel Image Denoising
IEEE Transactions on Signal Processing - Part II
Asymptotic decorrelation of between-Scale Wavelet coefficients
IEEE Transactions on Information Theory
Noise Covariance Properties in Dual-Tree Wavelet Decompositions
IEEE Transactions on Information Theory
Multiscale MAP filtering of SAR images
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
Image denoising using scale mixtures of Gaussians in the wavelet domain
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
Image analysis using a dual-tree M-band wavelet transform
IEEE Transactions on Image Processing
The Undecimated Wavelet Decomposition and its Reconstruction
IEEE Transactions on Image Processing
A New SURE Approach to Image Denoising: Interscale Orthonormal Wavelet Thresholding
IEEE Transactions on Image Processing
The SURE-LET Approach to Image Denoising
IEEE Transactions on Image Processing
Image Modeling Using Interscale Phase Properties of Complex Wavelet Coefficients
IEEE Transactions on Image Processing
Image Denoising in Mixed Poisson–Gaussian Noise
IEEE Transactions on Image Processing
IEEE Transactions on Information Theory
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We present a second order statistical analysis of the 2D Discrete Wavelet Transform (2D DWT) coefficients. The input images are considered as wide sense bivariate random processes. We derive closed form expressions for the wavelet coefficients@? correlation functions in all possible scenarios: inter-scale and inter-band, inter-scale and intra-band, intra-scale and inter-band and intra-scale and intra-band. The particularization of the input process to the White Gaussian Noise (WGN) case is considered as well. A special attention is paid to the asymptotical analysis obtained by considering an infinite number of decomposition levels. Simulation results are also reported, confirming the theoretical results obtained. The equations derived, and especially the inter-scale and intra-band dependency of the 2D DWT coefficients, are useful for the design of different signal processing systems as for example image denoising algorithms. We show how to apply our theoretical results for designing state of the art denoising systems which exploit the 2D DWT.