Image Denoising With 2D Scale-Mixing Complex Wavelet Transforms

This paper introduces an image denoising procedure based on a 2D scale-mixing complex-valued wavelet transform. Both the minimal (unitary) and redundant (maximum overlap) versions of the transform are used. The covariance structure of white noise in wavelet domain is established. Estimation is performed via empirical Bayesian techniques, including versions that preserve the phase of the complex-valued wavelet coefficients and those that do not. The new procedure exhibits excellent quantitative and visual performance, which is demonstrated by simulation on standard test images.

[1]  R. DeVore,et al.  Hyperbolic Wavelet Approximation , 1998 .

[2]  Jean-Marc Lina,et al.  Image Processing with Complex Daubechies Wavelets , 1997, Journal of Mathematical Imaging and Vision.

[3]  Vyacheslav Zavadsky.  Image Approximation by Rectangular Wavelet Transform , 2007, Journal of Mathematical Imaging and Vision.

[4]  Brani Vidakovic,et al.  A wavelet‐based spectral method for extracting self‐similarity measures in time‐varying two‐dimensional rainfall maps , 2011 .

[5]  Eero P. Simoncelli,et al.  Image quality assessment: from error visibility to structural similarity , 2004, IEEE Transactions on Image Processing.

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

[7]  Levent Sendur,et al.  Bivariate shrinkage functions for wavelet-based denoising exploiting interscale dependency , 2002, IEEE Trans. Signal Process..

[8]  Nick G. Kingsbury,et al.  Hidden Markov tree modeling of complex wavelet transforms , 2000, 2000 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.00CH37100).

[9]  B. Silverman,et al.  Wavelet thresholding via a Bayesian approach , 1998 .

[10]  Justin K. Romberg,et al.  Bayesian tree-structured image modeling using wavelet-domain hidden Markov models , 2001, IEEE Trans. Image Process..

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

[12]  Patrick Flandrin,et al.  Wavelet analysis and synthesis of fractional Brownian motion , 1992, IEEE Trans. Inf. Theory.

[13]  Richard G. Baraniuk,et al.  A Hidden Markov Tree Model for the Complex Wavelet Transform , 2001 .

[14]  D. Donoho,et al.  Translation-Invariant De-Noising , 1995 .

[15]  Efstathios Paparoditis,et al.  Wavelet Methods in Statistics with R , 2010 .

[16]  G. Nason,et al.  Real nonparametric regression using complex wavelets , 2004 .

[17]  Alessandro Foi,et al.  Image Denoising by Sparse 3-D Transform-Domain Collaborative Filtering , 2007, IEEE Transactions on Image Processing.

[18]  Jean-Marc Lina,et al.  Nonlinear shrinkage estimation with complex Daubechies wavelets , 1997, Optics & Photonics.

[19]  Jean-Marc Lina,et al.  Complex Dyadic Multiresolution Analyses , 1999 .

[20]  M. Clyde,et al.  Multiple shrinkage and subset selection in wavelets , 1998 .

[21]  Michael R. Chernick,et al.  Wavelet Methods for Time Series Analysis , 2001, Technometrics.

[22]  Diego Clonda,et al.  Complex Daubechies wavelets: properties and statistical image modelling , 2004, Signal Process..

[23]  Rainer von Sachs,et al.  Wavelet thresholding in anisotropic function classes and application to adaptive estimation of evolutionary spectra , 1997 .

[24]  H. Chipman,et al.  Adaptive Bayesian Wavelet Shrinkage , 1997 .

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

[26]  Stuart Barber,et al.  Denoising Real Images Using Complex-Valued Wavelets , 2003 .

[27]  Patrice Abry,et al.  Self-Similar Anisotropic Texture Analysis: The Hyperbolic Wavelet Transform Contribution , 2013, IEEE Transactions on Image Processing.

[28]  Brani Vidakovic,et al.  Bayesian Wavelet Shrinkage Strategies: A Review , 2013 .