Real and Complex Valued Ripplet-I Transform for Medical Image Denoising and Analysis of Thresholding Constants and Scales Effects

  • Hüseyin Yaşar Ministry of Health of the Republic of Turkey
  • Murat Ceylan Department of Electrical and Electronics Engineering, Selcuk University, Konya, Turkey
Keywords: Real and complex valued ripplet-I transform, Medical image denoising, Thresholding constant, Peak signal-to-noise ratio (PSNR), Mean structural similarity index (MSSIM), Feature similarity index (FSIM)


Medical image processing is an important diagnostic tool in the field of medical. Medical images might be affected by the noises that manipulate the resolution negatively during screening or transmission. These images need to be eliminated so as not to affect the diagnosis success negatively. In medical image denoising studies, using the multi-resolution analysis coefficients is a widely appreciated method. This study tested the success rate of real and complex valued ripplet-I transform for medical image denoising. Thanks to this study, the complex version of the newly suggested ripplet-I transform whose real version was used formerly in various studies was used in a medical image denoising application the first time. In the study tested with 40 liver images, 40 retinal images and 322 mammographic images, peak signal-to-noise ratio (PSNR), mean structural similarity index (MSSIM) and feature similarity index (FSIM) were utilized to compare the successes of image denoising. In the wake of study, it was seen that the complex valued ripplet-I (CVR-I) transform gave better results than the real valued ripplet-I (RVR-I) transform when used in the same image denoising algorithm. This study also examined the effects that the changes in scale and thresholding constant values have on the medical image denoising results, thus making this study appear as a guideline.


(1) Reider, P. and Nossek, J. A. Implementation of orthogonal wavelet transforms and their applications. in Application-Specific Systems, Architectures and Processors, 1997. Proceedings. IEEE International Conference on.

(2) Pu-chun, C., et al., Application of Debauchies wavelet to the de-noising of radio maps. Chinese Astronomy and Astrophysics, 2001. 25(1): p. 132-137.

(3) Zhai, J. and Zhang, S. Image denoising via wavelet threshold: single wavelet and multiple wavelets transform. in Machine Learning and Cybernetics, 2005. Proceedings of 2005 International Conference on.

(4) Li, X. and Zhu, S. Image denoising based on wavelet domain spatial context modeling. in Intelligent Control and Automation, 2006. WCICA 2006. The Sixth World Congress on.

(5) Junli, L., et al. A novel method for the determination of the wavelet denoising threshold. in Bioinformatics and Biomedical Engineering, 2007. ICBBE 2007. The 1st International Conference on.

(6) Hongqiao, L. and Shengqian, W. A new image denoising method using wavelet transform. in Information Technology and Applications, 2009. IFITA'09. International Forum on.

(7) Wang, X. Y., et al., A new wavelet-based image denoising using undecimated discrete wavelet transform and least squares support vector machine. Expert Systems with Applications, 2010. 37(10): p. 7040-7049.

(8) Chen, G., et al., Wavelet-based image denoising using three scales of dependency. IET Image Process, 2012. 6(6): p. 756-760.

(9) Chen, G., et al. Wavelet-based denoising: a brief review. in Intelligent Control and Information Processing (ICICIP), 2013 Fourth International Conference on.

(10) Candes, E. J. and Donoho, D. L., Ridgelets: the key to high-dimensional intermittency. Philosophical Transactions Royal Society, 1999. 357: p. 2495-2509.

(11) Candes, E. J. and Donoho, D. L., Curvelets-A surprisingly effective nonadaptie representation for objects with edges. Chap. Curves and Surface Fitting, A. Cohen, C. Rabut, L. Schumaker, Editors 1999. p. 105-120.

(12) Starck, J. L., et al., The curvelet transform for image denoising. IEEE Transactions on Image Processing, 2002. 11(6): p. 670-684.

(13) Sivakumar, R., Denoising of computer tomography images using curvelet transform. ARPN Journal of Engineering and Applied Sciences, 2007. 2(1): p. 21-26.

(14) Ma, L., et al., Pixel fusion based curvelets and wavelets denoise algorithm. Engineering Letters, 2007. 14(2): p. 130-134.

(15) Ali, F. E., et al., Curvelet fusion of MR and CT images. Progress In Electromagnetics Research C, 2008. 3: p. 215-224.

(16) Reddy, G. J., et al., Fingerprint image denoising using

curvelet transform. ARPN Journal of Engineering and Applied Sciences, 2008. 3(3): p. 31-35.

(17) Patil, A. A. and Singhai, J., Image denoising using curvelet transform: an approach for edge preservation. Journal of Scientific & Industrial Research, 2010. 69: p. 34-38.

(18) Binh, N. T. and Khare, A., Multilevel threshold based image denoising in curvelet domain. Journal of Computer Science and Technology, 2010. 25(3): p. 632-640.

(19) Shukla, M. and Changlani, S., A comparative study of wavelet and curvelet transform for image denoising. IOSR Journal of Electronics and Communication Engineering, 2013. 7(4): p. 63-68.

(20) Candes, E. J. and Donoho, D. L., New tight frames of curvelets and optimal representations of objects with piecewise-C2 singularities. Communications on Pure and Applied Mathematics, 1999. 57(2): p. 219-266.

(21) Candes, E. J. and Guo, F., New multiscale transforms, minimum total variation synthesis: application to edge-preserving image reconstruction. Sig. Process., special issue on Image and Video Coding Beyond Standards, 2002. 82(11): p. 1519-1543.

(22) Lawton, W., Applications of complex valued wavelet transforms to subband decomposition. IEEE Trans. Signal Processing, 1993. 41(12): p. 3566-3568.

(23) Lina, J. M., Complex Daubechies wavelets: filter design and applications. Inverse Problems, Tomography, and Image Processing, 1998. p. 95-112.

(24) Selesnick, I. W., et al., The dual-tree complex wavelet transform. IEEE Signal Processing Magazine, 2005. 22(6): p. 123-151.

(25) Aryaz, B. and Runyi, Y. A dual-tree complex wavelet with application in image denoising. in Signal Processing and Communications, 2007. ICSPC 2007. IEEE International Conference on.

(26) Jingyu, Y., et al. 2-D anisotropic dual-tree complex wavelet packets and its application to image denoising. in Image Processing, 2008. ICIP 2008. 15th IEEE International Conference on.

(27) Song, Z. and Yuanpeng, L. A novel image denosing scheme via combining dual-tree complex wavelet transform and bandelets. in Intelligent Information Technology Application, 2009. IITA 2009. Third International Symposium on.

(28) Candes, E. J., Fast discrete curvelet transforms. Multiscale Modeling & Simulation, 2006. 5(3): p. 861-899.

(29) Neelamani, R., et al., Complex curvelet-based adaptive subtraction of several noise templates. in SEG Technical Program Expanded Abstracts 2008. Society of Exploration Geophysicists.

(30) Neelamani, R., et al., Adaptive subtraction using complex curvelet transform. in 70th EAGE Conference and Exhibition incorporating SPE EUROPEC 2008.

(31) Neelamani, R., et al., Adaptive subtraction using complex-valued curvelet transform. Geophysics, 2010. 75(4): p. V51-V60.

(32) Yan, H., et al. Image restoration using Gaussian scale mixtures in complex curvelet transform domain. in Measuring Technology and Mechatronics Automation (ICMTMA), 2010 International Conference on.

(33) Xu, J., et al., Ripplet: A new transform for image processing. Journal of Visual Communication and Image Representation, 2010. 21(7): p. 627-639.

(34) Gupta, D., et al., Ripplet domain non-linear filtering for speckle reduction in ultrasound medical images. Biomedical Signal Processing and Control, 2014. 10: p. 79-91.

(35) Yaşar, H. and Ceylan, M. New approaches based on real and complex forms of ripplet-I transform for image analysis, in Signal Processing and Communication Application Conference,

(36) Ceylan, M. and Yaşar, H., A novel approach for automatic blood vessel extraction in retinal images: complex ripplet-I transform and complex valued articial neural network. Turkish Journal of Electrical Engineering and Computer Sciences, 2016.

(4): p. 3212--3227.

(37) Yaşar, H., Analysis of medical images with multi-resolution methods, MA thesis, The Graduate School of Natural and Applied of Selcuk University, Advisor: M. Ceylan, 2015.

(38) (accessed 18 February 2017).

(39) (accessed 18 February 2017).

(40) Bao, O. Z., et al., Local adaptive shrinkage threshold denoising using curvelet coefficients. Electronics Letters, 2008. 44(4): p. 277-278.

(41) Staal, J., et al., Ridge based vessel segmentation in color images of the retina. IEEE Transactions on Medical Imaging, 2004. 23(4): p. 501-509.

(42) Suckling, J., et al., The mammographic image analysis society digital mammogram database, in Exerpta Medica. International Congress Series, 1994.

(43) Wang, Z. et al., Image quality assessment: from error measurement to structural similarity. IEEE Trans. Image Processing, 2004. 13(4): p. 600-612.

(44) Thakur, N. and Devi, S.; A new method for color image quality assessment. International Journal of Computer Applications, 2011. 15(2):p. 10-17.

(45) Zhang, L. et al., FSIM: A feature similarity index for image quality assessment. IEEE Trans. Image Processing, 2011. 20(8): p. 2378-2386.

How to Cite
Yaşar, H., & Ceylan, M. (2017). Real and Complex Valued Ripplet-I Transform for Medical Image Denoising and Analysis of Thresholding Constants and Scales Effects. Journal of Biomedical Engineering and Medical Imaging, 4(2), 10.