Wavelet domain denoising of single-band and multiband images adapted to the probability of the presence of features of interest

We study an image denoising approach the core of which is a locally adaptive estimation of the probability that a given coefficient contains a significant noise-free component, which we call "signal of interest". We motivate this approach within the minimum mean squared error criterion and develop and analyze different locally adaptive versions of this method for color and for multispectral images in remote sensing. For color images, we study two different approaches: (i) using a joint spatial/spectral activity indicator in the RGB color space and (ii) componentwise spatially adaptive denoising in a luminance-chrominance space. We demonstrate and discuss the advantages of both of these approaches in different scenarios. We also compare the analyzed method to other recent wavelet domain denoisers for multiband data both on color and on multispectral images.

[1]  Edward H. Adelson,et al.  Noise removal via Bayesian wavelet coring , 1996, Proceedings of 3rd IEEE International Conference on Image Processing.

[2]  Aleksandra Pizurica,et al.  A joint inter- and intrascale statistical model for Bayesian wavelet based image denoising , 2002, IEEE Trans. Image Process..

[3]  Stéphane Mallat,et al.  Bandelet Image Approximation and Compression , 2005, Multiscale Model. Simul..

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

[5]  Kannan Ramchandran,et al.  Low-complexity image denoising based on statistical modeling of wavelet coefficients , 1999, IEEE Signal Processing Letters.

[6]  Stephen C. Cain,et al.  Sampling, radiometry, and image reconstruction for polar and geostationary meteorological remote sensing systems , 2002, SPIE Optics + Photonics.

[7]  David Middleton,et al.  Simultaneous optimum detection and estimation of signals in noise , 1968, IEEE Trans. Inf. Theory.

[8]  Brani Vidakovic,et al.  Wavelet-Based Nonparametric Bayes Methods , 1998 .

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

[10]  Martin Vetterli,et al.  Adaptive wavelet thresholding for image denoising and compression , 2000, IEEE Trans. Image Process..

[11]  D. D.-Y. Po,et al.  Directional multiscale modeling of images using the contourlet transform , 2006, IEEE Transactions on Image Processing.

[12]  S. Mallat,et al.  Minimax Restoration and Deconvolution , 1999 .

[13]  Aleksandra Pizurica,et al.  FPGA Design and Implementation of a Wavelet-Domain Video Denoising System , 2005, ACIVS.

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

[15]  I. Johnstone,et al.  Empirical Bayes selection of wavelet thresholds , 2005, math/0508281.

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

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

[18]  Aleksandra Pizurica,et al.  A versatile wavelet domain noise filtration technique for medical imaging , 2003, IEEE Transactions on Medical Imaging.

[19]  S. Mallat.  A wavelet tour of signal processing , 1998 .

[20]  Maarten Jansen,et al.  Noise Reduction by Wavelet Thresholding , 2001 .

[21]  Eero P. Simoncelli,et al.  Image Denoising using Gaussian Scale Mixtures in the Wavelet Domain , 2002 .

[22]  Sailes K. Sengupta,et al.  Bayesian Inference in Wavelet-Based Models , 2002, Technometrics.

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

[24]  Emmanuel J. Candès,et al.  The curvelet transform for image denoising , 2002, IEEE Trans. Image Process..

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

[26]  Aleksandra Pizurica,et al.  Estimating the probability of the presence of a signal of interest in multiresolution single- and multiband image denoising , 2006, IEEE Transactions on Image Processing.

[27]  Kannan Ramchandran,et al.  On multivariate estimation by thresholding , 2003, Proceedings 2003 International Conference on Image Processing (Cat. No.03CH37429).

[28]  E. Candès,et al.  Curvelets: A Surprisingly Effective Nonadaptive Representation for Objects with Edges , 2000 .

[29]  Paul Scheunders,et al.  Least-squares interband denoising of color and multispectral images , 2004, 2004 International Conference on Image Processing, 2004. ICIP '04..

[30]  I. Selesnick,et al.  Bivariate shrinkage with local variance estimation , 2002, IEEE Signal Processing Letters.

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

[32]  Amel Benazza-Benyahia,et al.  Building robust wavelet estimators for multicomponent images using Stein's principle , 2005, IEEE Transactions on Image Processing.

[33]  Bin Yu,et al.  Wavelet thresholding via MDL for natural images , 2000, IEEE Trans. Inf. Theory.

[34]  Paul Scheunders,et al.  Wavelet thresholding of multivalued images , 2004, IEEE Transactions on Image Processing.

[35]  Ram M. Narayanan,et al.  Noise estimation in remote sensing imagery using data masking , 2003 .

[36]  Thomas S. Huang,et al.  Image processing , 1971 .

[37]  Martin Vetterli,et al.  Spatially adaptive wavelet thresholding with context modeling for image denoising , 1998, Proceedings 1998 International Conference on Image Processing. ICIP98 (Cat. No.98CB36269).