Multilevel adaptive thresholding and shrinkage technique for denoising using Daubechies complex wavelet transform

REFERENCES

• Donoho, D. L. Denoising by soft-thresholding. IEEE Trans. Inf. Theory, 1995, 41, 613–627.
   Web of Science ®Google Scholar
• Khare, A. and Tiwary, U. S. A new method for deblurring and denoising of medical mages using complex wavelet transform, Proc. 27th Annual Int. Conf. of IEEE-EMBS, Shanghai, China, September 2005, IEEE, pp. 1897–1900.
   Google Scholar
• Khare, A. and Tiwary, U. S. Soft-thresholding for denoising of medical images — a multiresolution approach. Int. J. Wavelets Multiresolution Inf. Process., 2005, 3, 477–496.
   Web of Science ®Google Scholar
• Strang, G. Wavelets and dilation equations: a brief introduction. SIAM Rev., 1989, 31, 614–627.
   Web of Science ®Google Scholar
• Gopinath, R. A. The phaselet transform — an integral redundancy nearly shift-invariant wavelet transform. IEEE Trans. Signal Process., 2003, 51, 1792–1805.
   Web of Science ®Google Scholar
• Nason, G. P. and Silverman, B. W. The stationary wavelet transform and some statistical applications. Lect. Notes Stat., 1995, 103, 281–299.
   Google Scholar
• Coifman, R. R. and Donoho, D. L. Translationinvariant denoising. Lect. Notes Stat., 1995, 103, 125–150.
   Google Scholar
• Simoncelli, E. P., Freeman, W. T., Adelson, E. H. and Heeger, D. J. Shiftable multiscale transforms. IEEE Trans. Inf. Theory, 1992, 38, 5587–5607.
   Google Scholar
• Laine, A. and Chang, C.-M. Denoising via wavelet transforms using steerable filters, Proc. IEEE Int. Symp. on Circuits and systems: ISCAS ’95, Seattle, WA, USA, April-May 1995. IEEE, pp. 1956–1959.
   Google Scholar
• Selesnick, I. W., Baraniuk, R. G. and Kingsbury, N. The dual-tree complex wavelet transform — a coherent framework for multiscale signal and image processing. IEEE Signal Process. Mag., 2005, 22, 123–151.
   Web of Science ®Google Scholar
• Fernandes, F. C. A., Spaendonck, R. L. C. and Burrus, C. S. A new framework for complex wavelet transform. IEEE Trans. Signal Process., 2003, 51, 1825–1837.
   Web of Science ®Google Scholar
• Lawton, W. Applications of complex valued wavelet transform in subband decomposition. IEEE Trans. Signal Process., 1993, 41, 3566–3568.
   Web of Science ®Google Scholar
• Lina, J.-M. and Mayrand, M. Complex Daubechies wavelets. Appl. Comput. Harmon. Anal., 1995, 2, 219– 229.
   Web of Science ®Google Scholar
• Jalobeanu, A., Feraud, L. B. and Zerubia, J. ‘Satellite image deconvolution using complex wavelet packets ’, Report 3955, INRIA, Le Chesnay Cedex, France, 2000.
   Google Scholar
• Daubechies, I. Ten Lectures on Wavelets, 1992 (SIAM, Philadelphia, PA).
   Google Scholar
• Strang, G. and Nguyen, T. Wavelets and Filter Banks, 1996 (Wellesley-Cambridge Press: Wellesley, MA).
   Google Scholar
• Zhang, X.-P., Desai, M. D. and Peng, Y.-N. Orthonormal complex filter banks and wavelets: some properties and design. IEEE Trans. Signal Process., 1999, 47, 1039–1048.
   Web of Science ®Google Scholar
• Clonda, D., Lina, J.-M. and Goulard, B. Complex Daubechies wavelets: properties and statistical image modeling. Signal Process., 2004, 84, 1–23.
   Web of Science ®Google Scholar
• Jalobeanu, A., Kingsbury, N. and Zerubia, J. Image deconvolution using Markov tree modeling of complex wavelet packets, Proc. IEEE Int. Conf. on Image processing: ICIP’01, Tessaloniki, Greece, October 2001, IEEE, pp. 201–204.
   Google Scholar
• Lina, J.-M. and MacGibbon, B. Non-linear shrinkage estimation with complex Daubechies wavelets. Proc. SPIE, 1997, 3159, 67–79.
   Google Scholar
• Kingsbury, N. Image processing with complex wavelets. Philos. Trans. R. Soc. Lond. A, 1999, 357A, 2543–2560.
   Google Scholar
• Romberg, J. K., Choi, H., Baraniuk, R. G. and Kingsbury, N. ‘A hidden Markov tree model for the complex wavelet transform’, http://www.acm.cake-ch.edu/yjrom/publications/complexHMTv2.pdf
   Google Scholar
• Simoncelli, E. P. Bayesian denoising of visual images in the wavelet domain. Lect. Notes Stat., 1999, 141, 291–308.
   Google Scholar
• Khare, A., Khare, M., Jeong, Y., Kim, H. and Jeon, M. Despeckling of medical ultrasound images using complex wavelet transform based Bayesian shrinkage. Signal Process., 2010, 90, 428–439.
   Web of Science ®Google Scholar
• Donoho, D. L. and Johnstone, I. M. Ideal spatial adaptation via wavelet shrinkage. Biometrica, 1994, 81, 425–455.
   Web of Science ®Google Scholar
• Portilla, J., Strela, V., Wainwright, M. J. and Simoncelli, E. P. Image denoising using scale mixtures of Gaussians in the wavelet domain. IEEE Trans. Image Process, 2003, 12, 1338–1351.
   PubMed Web of Science ®Google Scholar
• Blu, T. and Luisier, F. The SURE-LET approach to image denoising. IEEE Trans. Image Process., 2007, 16, 2778–2786.
   PubMed Web of Science ®Google Scholar
• Choi, H. and Romberg, J. ‘Software for image denoising using wavelet-domain hidden Markov tree models’, http://www-dsp.rice.edu/software/WHMT/whmt1.zip
   Google Scholar
• Wickerhauser, M. V. Adapted Wavelet Analysis from Theory to Software, 1994 (AK Peters Ltd, Wellesley, MA).
   Google Scholar
• Xu, Y., Weaver, J. B., Healy, D. M. and Lu, J. Wavelet transform domain filters: a spatially selective noise filtration technique. IEEE Trans. Image Process., 1998, 3, 133–155.
   Google Scholar
• Wavelab 802. http://www-stat.stanford.edu/ ~wavelab
   Google Scholar