Reverse Biorthogonal Spline Wavelets in Undecimated Transform for Image Denoising
DOI:
https://doi.org/10.26438/ijcse/v6i2.6672Keywords:
Reverse biorthogonal, Spline, Undecimated Transform, Image detailAbstract
Reverse biorthogonal wavelets are highly regular wavelets with compact support and symmetric filters and they have explicit construction. This paper explores the performance of the reverse biorthogonal spline wavelets in denoising images differentiated by the detail-contents in the images. The transform used in the study is the Undecimated Wavelet Transform which is a translation-invariant transform. The selected images are corrupted by adding white Gaussian noise to produce noisy test images. The study shows that the denoising effect depends on the amount of details in the image. It is also seen that reverse biorthogonal spline wavelets are highly effective in denoising dense-detail images like fingerprints. These wavelets also give good denoising for low-detail images like human face. The best wavelet in the family for each of these purposes has been sorted out. Rbio 3.1 is found to be an odd member of the family. These wavelets are found to give poor results in denoising medium-detail images. The study finds application in Forensic science and in restoration of facial images and when the images encountered in such applications contain several types of noise distributions simultaneously.
References
I. Daubechies,“Orthonormal Bases of Ccompactly Supported Wavelets”, Communications on Pure and Applied Mathematics. XLI, pp. 909-996, 1988
G. Strang, T. Nguyen, “Wavelets and filter banks”, Wellesley-Cambridge Press, Wellesley, pp.xi-71,1996.
Y.S. Bahendwar, G.R. Sinha, “Mathematical Methods and Systems in Science and Engineering”, WSEAS Press, Spain, pp.158 – 162, 2015.
J. Kaur, R. Kaur, “Biomedical Images Denoising Using Symlet Wavelet with Wiener Filter”. International Journal of Engineering Research and Applications (IJERA), Vol. 3, No. 3, pp. 548-550, 2013
L. Renjini, R.L. Jyothi, “Wavelet Based Image Analysis: a Comprehensive Survey”, International Journal of Computer Trends and Technology (IJCTT), Vol. 21, No.3, pp.134-140, 2015
M. Unser, “Ten Good Reasons for Using Spline Wavelets.” Proceedings of SPIE, Wavelets Applications in Signal and Image Processing V, 3169, pp. 422-431, 1997.
P.P. Vaidyanathan, I. Djokovic, “An Introduction to Wavelet Transforms”, California Institute of Technology, Pasadena, pp. 1-116, 1994.
A. Cohen, I. Daubechies, J.C. Feauveau, “Biorthogonal Bases of Compactly Supported Wavelets”, Communications on Puree and Applied Mathematics, XLV, pp. 485-560, 1992
M. Vetterli, C. Herley, “Wavelets and Filter Banks: Ttheory and Design”, IEEE Transactions on Signal Processing, Vol. 40, No. 9, pp. 2207-2232, 1992.
L. Passrija, A.S. Virk, M. Kaur, “Performance Evaluation of Image Enhancement Techniques in Spatial and Wavelet Domains”, International Journal of Computers & Technology, Vol.3, No.1, pp. 162-166, 2012.
P. Rakheja, R. Vig, “Image Denoising Using Combination of Median Filtering and Wavelet Transform”, International Journal of Computer Applications, Vol. 141, No.9, pp. 31-35, 2016
T.N. Tilak, S. Krishnakumar, “Effectiveness of Symlets in De-noising Fingerprint Images”, International Journal of Computer Science and Engineering, Vol. 3, No.12, pp. 29-34, 2015.
R.R. Coifman, D.L. Donoho, “Translation-Invariant Denoising”, Stanford University, California, pp. 1-26, 1995.
J.L. Starck, J. Fadili, F. Murtagh, “The Undecimated Wavelet Decomposition and Its Reconstruction”, IEEE Transactions on Image Processing, Vol.16, No.2, pp. 297-309, 2007.
I.W. Selesnick, “The Double-Density Dual-Tree DWT”, IEEE Transactions on Signal Processing, Vol. 52, No.5, pp. 1304-1314, 2004.
G.P. Nason, B.W. Silverman, “Wavelets and statistics”, Springer-Verlag, New York, pp. 281–299, 1995.
S.G. Chang, B. Yu, M. Vetterli, “Adaptive Wavelet Thresholding for Image Denoising and Compression”, IEEE Transactions on Image Processing, Vol.9, No.9, pp. 1532-1546, 2000.
W. Qian, “Research on Image Denoising With an Improved Wavelet Threshold Algorithm”, International Journal of Signal Processing, Image Processing and Pattern Recognition, Vol.8, No.9, pp. 257-266, 2015.
L. Gabralla, H. Mahersia, M. Zaroug, “Denoising CT Images Using Wavelet Transform”, International Journal of Advanced Computer Science and Applications (IJACSA), Vol.6, No.5, pp.125-129, 2015.
L. Yuan, J. Wu, S. Li, “Improved Wavelet Threshold for Gray Scale Image Denoising”, International Journal of Signal Processing, Image Processing and Pattern Recognition, Vol.7, No.3, pp. 45-52, 2014.
Anutam, Rajini, “Comparative Analysis of Filters and Wavelet Based Thresholding Methods for Image Denoising”, Computer Science & Information Technology (CS & IT). pp. 137–148, 2014.
K.V. Thakur, P.G. Ambhore, A.M. Sapkal, “Medical image denoising using rotated wavelet filter and bilateral filter”, IJAIS Proceedings of 7th International Conference on Communication Computing and Virtualization ICCCV, India, pp. 14-18, 2016.
H. Jagadish, J. Prakash, “A New Approach for Denoising Remotely Sensed Images Using DWT Based Homomorphic Filtering Techniques”, International Journal of Emerging Trends & Technology in Computer Science (IJETTCS), Vol.3, No.3, pp. 90-96, 2014.
S. Bhatnagar, R.C. Jain, “Application of Discrete Multi-Wavelet Transform in Denoising of Mammographic Images”, Indian Journal of Science and Technology, Vol.9, No.48, pp. 1-9, 2016.
Downloads
Published
How to Cite
Issue
Section
License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors contributing to this journal agree to publish their articles under the Creative Commons Attribution 4.0 International License, allowing third parties to share their work (copy, distribute, transmit) and to adapt it, under the condition that the authors are given credit and that in the event of reuse or distribution, the terms of this license are made clear.
