{"title":"Synthesis of Wavelet Filters using Wavelet Neural Networks","authors":"Wajdi Bellil, Chokri Ben Amar, Adel M. Alimi","volume":13,"journal":"International Journal of Aerospace and Mechanical Engineering","pagesStart":195,"pagesEnd":199,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/9532","abstract":"An application of Beta wavelet networks to\r\nsynthesize pass-high and pass-low wavelet filters is investigated in\r\nthis work. A Beta wavelet network is constructed using a parametric\r\nfunction called Beta function in order to resolve some nonlinear\r\napproximation problem. We combine the filter design theory with\r\nwavelet network approximation to synthesize perfect filter\r\nreconstruction. The order filter is given by the number of neurons in\r\nthe hidden layer of the neural network. In this paper we use only the\r\nfirst derivative of Beta function to illustrate the proposed design\r\nprocedures and exhibit its performance.","references":"[1] W.Bellil, C.Ben Amar et M.Adel Alimi. \"Beta Wavelet Based Image\r\nCompression\", International Conference on Signal, System and Design,\r\nSSD03, Tunisia, vol. 1, pp. 77-82, Mars, 2003.\r\n[2] W.Bellil, C.Ben Amar, M.Zaied and M.Adel Alimi \"La fonction Beta et\r\nses d\u00e9riv\u00e9es : vers une nouvelle famille d-ondelettes\", First International\r\nConference on Signal, System and Design, SCS-04, Tunisia, vol. 1, P.\r\n201-207, Mars2004.\r\n[3] S. Mallat, Une exploration des signaux en Ondelettes, les \u00e9ditions de\r\nl-\u00e9cole polytechnique, 2000.\r\n[4] Y. Oussar, I. Rivals, L. Personnaz & G. Dreyfus \"Training Wavelet\r\nNetworks for Nonlinear Dynamic Input-Output Modeling.\"\r\nNeurocomputing, in press. 1998.\r\n[5] V.Kruger, Happe, A., Sommer, G.,\"Affine real-time face tracking using\r\na wavelet network\", Proc. Workshop on Recognition, Analysis, and\r\nTracking of Faces and Gestures in Real-Time Systems, 26-27 (Corfu),\r\nIEEE, 141-8 (1999).\r\n[6] Q. Zhang and A. Benveniste, Wavelet Networks, IEEE Trans. on Neural\r\nNetworks 3 (6) 889-898, (1992).\r\n[7] N. Sebe, et al. \"Color indexing using wavelet-based salient points\". In\r\nIEEE Workshop on Content-based Access of Image and Video Libraries,\r\npages 15-19, 2000.\r\n[8] S.M. Smith and J.M. Brady. A new approach to low level image\r\nprocessing. Int. Journal of computer Vision, Vol. 23, No. 1, pp. 45-78,\r\n1997.\r\n[9] S. Bres, J.M. Jolion, Detection of Interest Points for Image Indexation,\r\n3rd Int. Conf. on Visual Information Systems, Visual99, pp. 427-434,\r\nJune 2-4 1999.\r\n[10] N C. Schmid, R. Mohr and C. Bauckhage, Comparing and Evaluating\r\nInterest Points, 6th International Conference on Computer Vision,\r\nBombay, India, January 1998.\r\n[11] A. Graps, An Introduction to Wavelets. In IEEE Computational Science\r\nand Engineering, 1995.\r\n[12] J. Crowley and A. Sanderson, Multiple Resolution Representation and\r\nProbabilistic Matching of 2-D Gray-Scale Shape, IEEE Transactions on\r\nPattern Analysis and Machine Intelligence, Vol. 9, No. 1, pp. 113-121,\r\n1987.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 13, 2008"}