Spatially adaptive wavelet thresholding with context modeling for image denoising

The method of wavelet thresholding for removing noise, or denoising, has been researched extensively due to its effectiveness and simplicity. Much of the work has been concentrated on finding the best uniform threshold or best basis. However, not much has been done to make this method adaptive to spatially changing statistics which is typical of a large class of images. This work proposes a spatially adaptive wavelet thresholding method based on context modeling, a common technique used in image compression to adapt the coder to the non-stationarity of images. We model each coefficient as a random variable with the generalized Gaussian prior with unknown parameters. Context modeling is used to estimate the parameters for each coefficient, which are then used to adapt the thresholding strategy. Experimental results show that spatially adaptive wavelet thresholding yields significantly superior image quality and lower MSE than optimal uniform thresholding.

[1]  Jan Biemond,et al.  An optimal bit allocation algorithm for sub-band coding , 1988, ICASSP-88., International Conference on Acoustics, Speech, and Signal Processing.

[2]  Steven A. Orszag,et al.  CBMS-NSF REGIONAL CONFERENCE SERIES IN APPLIED MATHEMATICS , 1978 .

[3]  July , 1890, The Hospital.

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

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

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

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

[8]  Jelena Kovacevic,et al.  Wavelets and Subband Coding , 2013, Prentice Hall Signal Processing Series.

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

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

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

[12]  Ulrich Stadtmüller,et al.  Estimation of Heteroscedasticity in Regression Analysis , 1987 .

[13]  Jerome M. Shapiro,et al.  Embedded image coding using zerotrees of wavelet coefficients , 1993, IEEE Trans. Signal Process..

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

[15]  Raymond J. Carroll,et al.  Adapting for Heteroscedasticity in Linear Models , 1982 .

[16]  Antonio Ortega,et al.  Image Subband Coding Using Progressive Classification and Adaptive Quantization , 1997 .

[17]  Kannan Ramchandran,et al.  Spatially adaptive statistical modeling of wavelet image coefficients and its application to denoising , 1999, 1999 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings. ICASSP99 (Cat. No.99CH36258).

[18]  Antonio Ortega,et al.  Image subband coding using context-based classification and adaptive quantization , 1999, IEEE Trans. Image Process..

[19]  Martin Vetterli,et al.  Image denoising via lossy compression and wavelet thresholding , 1997, Proceedings of International Conference on Image Processing.

[20]  Martin Vetterli,et al.  Spatial adaptive wavelet thresholding for image denoising , 1997, Proceedings of International Conference on Image Processing.

[21]  Michael T. Orchard,et al.  Image coding based on mixture modeling of wavelet coefficients and a fast estimation-quantization framework , 1997, Proceedings DCC '97. Data Compression Conference.