Multiple wavelet threshold estimation by generalized cross validation for images with correlated noise

Denoising algorithms based on wavelet thresholding replace small wavelet coefficients by zero and keep or shrink the coefficients with absolute value above the threshold. The optimal threshold minimizes the error of the result as compared to the unknown, exact data. To estimate this optimal threshold, we use generalized cross validation. This procedure does not require an estimation for the noise energy. Originally, this method assumes uncorrelated noise. In this paper, we describe how we can extend it to images with correlated noise.

[1]  Hervé Carfantan,et al.  Time-invariant orthonormal wavelet representations , 1996, IEEE Trans. Signal Process..

[2]  Michel Barlaud,et al.  Image coding using wavelet transform , 1992, IEEE Trans. Image Process..

[3]  Stéphane Mallat,et al.  Singularity detection and processing with wavelets , 1992, IEEE Trans. Inf. Theory.

[4]  M. Victor Wickerhauser,et al.  Adapted wavelet analysis from theory to software , 1994 .

[5]  Dennis M. Healy,et al.  Wavelet transform domain filters: a spatially selective noise filtration technique , 1994, IEEE Trans. Image Process..

[6]  Ingrid Daubechies,et al.  Ten Lectures on Wavelets , 1992 .

[7]  Grace Wahba,et al.  4. Estimating the Smoothing Parameter , 1990 .

[8]  G. Nason.  Wavelet Shrinkage using Cross-validation , 1996 .

[9]  B. Silverman,et al.  The Stationary Wavelet Transform and some Statistical Applications , 1995 .

[10]  G. Wahba.  Spline models for observational data , 1990 .

[11]  Stéphane Mallat,et al.  Characterization of Signals from Multiscale Edges , 2011, IEEE Trans. Pattern Anal. Mach. Intell..

[12]  I. Daubechies.  Orthonormal bases of compactly supported wavelets , 1988 .

[13]  Norman Weyrich,et al.  Wavelet shrinkage and generalized cross validation for image denoising , 1998, IEEE Trans. Image Process..

[14]  Truong Q. Nguyen,et al.  Wavelets and filter banks , 1996 .

[15]  Stéphane Mallat,et al.  A Theory for Multiresolution Signal Decomposition: The Wavelet Representation , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[16]  D. L. Donoho,et al.  Ideal spacial adaptation via wavelet shrinkage , 1994 .

[17]  Dirk Roose,et al.  Wavelet-based image denoising using a Markov random field a priori model , 1997, IEEE Trans. Image Process..

[18]  A. Cohen.  Ten Lectures on Wavelets, CBMS-NSF Regional Conference Series in Applied Mathematics, Vol. 61, I. Daubechies, SIAM, 1992, xix + 357 pp. , 1994 .

[19]  G. T. Warhola,et al.  DE-NOISING USING WAVELETS AND CROSS VALIDATION , 1995 .

[20]  I. Johnstone,et al.  Ideal spatial adaptation by wavelet shrinkage , 1994 .

[21]  I. Daubechies,et al.  Biorthogonal bases of compactly supported wavelets , 1992 .

[22]  I. Johnstone,et al.  Wavelet Shrinkage: Asymptopia? , 1995 .

[23]  I. Johnstone,et al.  Wavelet Threshold Estimators for Data with Correlated Noise , 1997 .

[24]  I. Johnstone,et al.  Adapting to Unknown Smoothness via Wavelet Shrinkage , 1995 .

[25]  Adhemar Bultheel,et al.  Generalized cross validation for wavelet thresholding , 1997, Signal Process..