Image denoising with neighbour dependency and customized wavelet and threshold

Image denoising by means of wavelet transforms has been an active research topic for many years. For a given noisy image, which kind of wavelet and what threshold we use should have significant impact on the quality of the denoised image. In this paper, we use Simulated Annealing to find the customized wavelet filters and the customized threshold corresponding to the given noisy image at the same time. Also, we propose to consider a small neighbourhood around the customized wavelet coefficient to be thresholded for image denoising. Experimental results show that our approach is better than VisuShrink, our NeighShrink with fixed wavelet, and the wiener2 filter that is available in Matlab Image Processing Toolbox. In addition, our NeighShrink with fixed wavelet already outperforms VisuShrink for all the experiments.

[1]  Ahmed H. Tewfik,et al.  Parametrization of compactly supported orthonormal wavelets , 1993, IEEE Trans. Signal Process..

[2]  Raghuveer M. Rao,et al.  Algorithms for designing wavelets to match a specified signal , 2000, IEEE Trans. Signal Process..

[3]  Gilbert Strang,et al.  Wavelets and Dilation Equations: A Brief Introduction , 1989, SIAM Rev..

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

[5]  Uday B. Desai,et al.  Search for optimal basis for signal denoising in the space of N-tap wavelets , 2001, Proceedings of the Sixth International Symposium on Signal Processing and its Applications (Cat.No.01EX467).

[6]  Deepen Sinha,et al.  On the optimal choice of a wavelet for signal representation , 1992, IEEE Trans. Inf. Theory.

[7]  Danny Coomans,et al.  Classification Using Adaptive Wavelets for Feature Extraction , 1997, IEEE Trans. Pattern Anal. Mach. Intell..

[8]  Robert D. Nowak,et al.  Wavelet-based statistical signal processing using hidden Markov models , 1998, IEEE Trans. Signal Process..

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

[10]  David L. Donoho,et al.  De-noising by soft-thresholding , 1995, IEEE Trans. Inf. Theory.

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

[12]  Hairong Qi,et al.  Face recognition using optimal non-orthogonal wavelet basis evaluated by information complexity , 2002, Object recognition supported by user interaction for service robots.

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

[14]  T. D. Bui,et al.  Image denoising using neighbouring wavelet coefficients , 2004, 2004 IEEE International Conference on Acoustics, Speech, and Signal Processing.

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

[16]  B. Silverman,et al.  Incorporating Information on Neighboring Coefficients Into Wavelet Estimation , 2001 .

[17]  Raghuveer M. Rao,et al.  Optimal matched wavelet construction and its application to image pattern recognition , 1995, Defense, Security, and Sensing.

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

[19]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[20]  T. D. Bui,et al.  Multiwavelets denoising using neighboring coefficients , 2003, IEEE Signal Processing Letters.

[21]  Stuart A. Golden,et al.  Identifying multiscale statistical models using the wavelet transform , 1991 .

[22]  W. Shengqian,et al.  Adaptive shrinkage de-noising using neighbourhood characteristic , 2002 .

[23]  John S. Baras,et al.  Constructing optimal wavelet basis for image compression , 1996, 1996 IEEE International Conference on Acoustics, Speech, and Signal Processing Conference Proceedings.

[24]  Tien D. Bui,et al.  Translation-invariant denoising using multiwavelets , 1998, IEEE Trans. Signal Process..