COMPARATIVE STUDY OF IMAGE PROCESSING USING WAVELET TRANSFORMS
Image processing based on the continuous or discrete image transforms is a classic technique. The image transforms are widely used in image filtering, data description, etc. In this paper, we focus on the comparison between numerical methods for image processing using different wavelets. So we build a numerical algorithm using Daubechies and Harr’s wavelets in denoising, compressing, restoring and segmentation numerical images.
wavelet transform, Daubechies wavelet, Haar’s wavelets, numerical images.
Received: April 26, 2021; Accepted: May 14, 2021; Published: June 15, 2021
How to cite this article: Mamadou M. Diop, Serigne Diouf and Alassane Sy, Comparative study of image processing using wavelet transforms, Far East Journal of Applied Mathematics 110(1)(2021), 27-47. DOI: 10.17654/AM110010027
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License
References
[1] S. Diouf, M. M. Diop and A. Sy, Image processing using non linear optimization, International Journal of Numerical Methods and Applications 21(1) (2021), 1-16. http://dx.doi.org/10.17654/NM020010001.[2] I. Daubechies, Orthonormal bases of compactly supported wavelets, Comm. Pure Appl. Math. 41(7) (1988), 909-996.[3] Lokenath Debanath, Wavelets transforms and their applications, Proc. Indian Nat. Sci. Acad. Part A 64 (1998), 685-713.[4] D. L. Donoho, Denoising via soft thresholding, IEEE Trans. Inform. Theory 41 (1996), 613-627.[5] C. Charles, Some wavelet applications to signal and image processing, Ph.D. Thesis, FUNDP, 2003.[6] C. Charles, G. Leclerc, J.-J. Pireaux and J.-P. Rasson, Wavelets applications in surface sciences: a comparison to Fourier transform, Surface and Interface Analysis 36 (2004), 49-60.[7] J. P. Cocquerez and S. Philipp, Analyse dimages : filtrage et segmentation, Masson, 1995.[8] I. Daubechies, M. Defrise and C. De Mol, An iterative thresholding algorithm for linear inverse problems with a sparsity constraint, Comm. Pure Appl. Math. 57 (2004), 1413-1457.[9] Yves Meyer, Wavelets and Operators, Cambridge University Press, 1992.[10] A. Haar, Zur Theorie der orthogonalen Funktionensysteme, Mathematische Annalen 69(3) (1910), 331-371.doi:10.1007/BF01456326,hdl:2027/uc1.b2619563.[11] A. Sy and D. Seck, Topological optimization with the p-Laplacian operator and an application in image processing, Bound. Value Probl. 2009, Art. ID 96813, 20 pp. http://doi.org/10.1155/2009/896813.[12] J. Weickert, Anisotropic diffusion in image processing, Ph.D. Thesis, University of Kaiserslautern, Germany, 1996.