Huseyin YASAR, Murat CEYLAN, Ayse Elif OZTURK

COMPARISON OF REAL AND COMPLEX-VALUED VERSIONS OF WAVELET TRANSFORM, CURVELET TRANSFORM AND RIDGELET TRANSFORM FOR MEDICAL IMAGE DENOISING

In this study; medical images were denoising with multiresolution analyses using real-valued wavelet transform (RVWT), complex-valued wavelet transform (CVWT), ridgelet transform (RT), real-valued first-generation curvelet transform (RVFG CT), real-valued second-generation curvelet transform (RVSG CT), complex-valued second-generation curvelet transform (CVSG CT) and results are compared. First and second-generation curvelet transformations are used for real- valued curvelet transform as two techniques. For the evaluation of the proposed system, we used 32 lung CT images. These images include 10 images with benign nodules and 22 images with malign nodules. Different types of noise like the Random noise, Gaussian noise and Salt & Pepper noise were added to these images and they are removed separately. The performances of used transforms are compared using Peak Signal to Noise Ratio (PSNR) parameter. Obtained results showed that complex-valued wavelet transform are suited for removal of random noise and Gaussian noise. In case of Gaussian noise in images, PSNRs of first generation curvelet transform and complex-valued wavelet transform are around 33 dB. The ridgelet transform provides high PSNR value (30.4dB) for denoising of salt & pepper noise in images.

Keywords:

Wavelet transform curvelet transform, ridgelet transform, denoising,

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Morlet J., Arehs G., Forugeau I., Giard D., “Wave Propagation and Sampling Theory”, Geophysics, vol. 47, pp. 203-236, 1982.
Morlet J., Arehs G., “Decompsotition Of Hardy Functions into Square Integrable Wavelets of Constant Shape”, SIAM J. Math. Anal., vol. 15, no. 4, p.p. 723-736, 1984.
Chuı C. K., Wu S., “An Introduction to Wavelets”, Academic Press, 1992. [4]
Cambridge Studies in Advanced Mathematics 37 , 1993.
Mallat S., “A Theory For Multiresolution Signal Decomposition: The Wavelet Representation”, IEEE Trans. Pattern Anal. Machine Intell., vol. 11, p.p. 674–693, 1989.
Daubechies I., “Ten Lectures on Wavelets”, PA: SIAM , Philadelphia, 1992.
Coifman R. R., Wickerhauser M. V., “Entropy Based Algorithms For Best Basis Selection”, IEEE Trans. On Information Theory, vol. 38, no. 2, 1992. [8] Lawton W., “Applications of Complex Valued Wavelet Transforms to Subband Decomposition”, IEEE Trans. Sig. Proc., vol. 41, no. 12, p.p. 3566- 3568,1993.
Lina J. M., “Complex Daubechies Wavelets: Filter Design and Applications”, Proc.ISAAC Conf., University of Delaware,1997.
Lang M., Guo H. and Odegard J. E., “Noise Reduction Using Undecimated Discrete Wavelet Transform”, IEEE Signal Processing Letters, 1995.
Mojsilovic A., Popovic M., Sevic D., “Classification of The Ultrasound Liver Images with The 2N X 1-D Wavelet Transform”, IEEE Int.Conf.Image, vol.1, p.p. 367-370, 1996.
Chang S.G., Yu B. and Vattereli M., “Adaptive Wavelet Thresholding for Image Denoising and Compression”, IEEE Trans. Image Processing, vol. 9, pp. 1532-1546, Sept. 2000.
Portilla J., Strela V., Wainwright M. J., Simoncelli, E.P., “Adaptive Wiener Denoising using a Gaussian Scale Mixture Model in The Wavelet Domain”, Proceedings of the 8th International Conference of Image Processing Thessaloniki, Greece, October 2001.
Chen G. Y. and Bui T. D., “”Multi-wavelet De-noising using Neighboring Coefficients”, IEEE Signal Processing Letters, vol. 10, no. 7, pp. 211- 214, 2003.
Abdulmunim M. E., “Color Image Denoising Using
Department of Computer Science, niversity of Technology, 2004.
Transform”, [16] Benjaminsen C., “Filtering of Periodic Noise Using the Complex Wavelet Transform”, M.Sc. thesis, Informatics and Mathematical Modelling, Technical University of Denmark, DTU, 2007.
Candes E., Donoho D. L., “Ridgelets: The Key to High-Dimensional Intermittency”, Phil. Trans. R. Soc. Lond. A., vol. 357, p.p. 2495–2509, 1999.
Do M. N. and Vetterli M., “The Fnite Ridgelet Transform For İmage Representation”, IEEE Transactions on Image Processing, vol. 12, no. 1, pp. 16-28, 2003.
Candes E. J., Donoho D. L., “Curvelets- A Surprisingly Effective Nonadaptie Representation For Objects With Edges in Curve and Surface Fitting”, In: A. Cohen, C. Rabut and L. Schumaker, Editors, Curves and Surface Fitting: Saint-Malo 1999, Vanderbilt University Press, Nashville, pp. 105–120, 2000.
Donoho D. L., Duncan M. R., “Digital Curvelet Transform: Strategy, Implementation and Experiments”, Proceeding of the SPIE on Wavelet Application VII, Orlando, p.p. 12-30, 2000.
Candes E.J., Demanet L., Donoho D.L., Ying L., “Fast Discrete Curvelet Transforms”, tech. rep., Applied
California Institute of Technology, pp. 1-44, 2005.
Mathematics, [22] Starck J. L., Candes E. J., Donoho D. L., “The Curvelet Transform For Image Denosing”, IEEE Trans. Image Processing., vol. 11, p.p. 131-141, 2002.
Gyaourova A. , Kamath C. and Fodor I. K., “Undecimated Curvelet Transforms For Image Denoising”,
Laboratory, Tech. Rep. UCRL-ID-150931, 2002. livermore
National [24] Sivakumar R., “Denoising of Computer Tomography Images using Curvelet Transform”, ARPN Journal of Engineering and Applied Sciences. February, 2007.
Rayudu D. K. V., Murala S. and Kumar V., “Denoising of Ultrasound Images Using Curvelet Transform”, The 2nd International Conference on Computer and Automation Engineering (ICCAE 2010), Singapore, vol. 3, pp. 447–451, 2010.
Li C., Liao X. and Yu J., “Complex-Valued Wavelet Network”, Journal of Computer and System Sciences, vol. 67, pp. 623-632, 2003.
Shukla P. D., “Complex Wavelet Transforms and Their Applications”, PhD Thesis, The University of Strathclyde, 2003.
Fernandes F., “Directional, Shift-İnsensitive, Complex Wavelet Transforms With Controllable Redundancy”, PhD Thesis, Rice University, 2002.
Strang G. and Hguyen T.,“Wavelets and Filter Banks”, Wellesley-Cambridge Press, 1996.
Oppenheim A.V. and Lim J.S., “The Importance Of Phase in Signals”, Proc. IEEE, vol. 69, pp. 529-541, 1981.
Lorenzetto G. P. and Kovesi P., “A Phase Based Image Comparison Technique”, DICTA99, University of Western Australia, 1999.
Driesen J. and Belmasn R., “Time-Frequency Analysis in Power Measurement Using Complex Wavelets”, IEEE Int. Sympo. On Circuits and Systems, ISCAS2002, pp. 681-684, 2002.
Lina J.M., “Image Processing With Complex Daubechies Wavelets”, Journal of Math. Imaging and Vision, vol. 7, pp. 211-223, 1997.
Bulow T. and Sommer G., “Hypercomplex Signals- A Novel Extension of The Analytic Signal to The Multidimensional Case”, IEEE Transactions on Signal Processing, vol. 49, pp. 2844-2852, 2001. [35] Selesnick I. W., Baraniuk R. G. and Kingsbury N. G., “The Dual-Tree Complex Wavelet Transform”, IEEE Signal Processing Magazine, vol.22, pp. 123-151, 2005. [36]
Thresholding”, IEEE Transactions On Information Theory, vol. 41, pp. 613-627, 1995. by Soft- [37]
Clinical H-Magnetic Resonance Spectroscopy And A Gallery Of Artifacts”, NMR in Biomedecine, vol. 17, no. 6, pp. 361-381, 2004. [38]
“Statistical Evaluation of Image Quality Measures”, Journal of Electronic Imaging, vol. 11, no. 2, pp. 206-223, 2002.
Farrell J. E., “Image Quality Evaluation in Colour
MacDonald, L.W. and Luo, M.R. (Eds.), John Wiley, pp. 285-313, 1999. And
Technology”. [40] Cadik M. and Slavik P., “Evaluation of Two Principal Approaches to Objective Image Quality Assessment”, 8th International Conference on Information Visualisation, IEEE Computer Society Press, pp. 513-551, 2004.
Nguyen,T.B. and Ziou, D., “Contextual and Non-Contextual Performance Evaluation of Edge Detectors”, Pattern Recognition Letters, vol. 21, no.9, pp. 805-816, 2000.
Elbadawy O., El-Sakka M. R. and Kamel M. S., “An Information Theoretic Image-Quality Measure”, Proceedings of the IEEE Canadian Conference
Engineering, vol. 1, pp. 169-172, 1998. and
Computer [43] Dosselmann R. and Yang X. D., “Existing And Emerging Image Quality Metrics”, Proceedings of the Canadian Conference on Electrical and Computer Engineering, pp. 1906-1913, 2006.
Ceylan M., “A New Complex-Valued Intelligent System Design on Evaulating of The Lung İmages With Computerized Tomography”, PhD Thesis, Selcuk University, Graduate School of Natural and Applied Sciences, May, 2009