FRAMES AND WAVELET TRANSFORMS ON TWO-DIMENSIONAL IMAGES

John Schmeelk

Title	FRAMES AND WAVELET TRANSFORMS ON TWO-DIMENSIONAL IMAGES
Publication Type	Journal Article
Year of Publication	2006
Authors	Schmeelk, J
Volume	10
Issue	1
Start Page	29
Pagination	14
Date Published	2006
ISSN	1083-2564
AMS	34A37
Abstract	The notion of frames is introduced in Hilbert Spaces. Wavelet analysis together with a brief description for the stability of images is introduced using wavelet transforms. The “control” is measured by the notion of a frame. Two wavelet transform examples are then presented and illustrated on a two dimensional image.
URL	http://www.acadsol.eu/en/articles/10/1/5.pdf
Refereed Designation	Refereed
Full Text	REFERENCES [1] E. Aboufadel and S. Schlicker, John Wiley and Sons, Inc., NY, 1999. [2] H.C. Andrews and B.R. Hunt, Digital Image Restoration, Prentice Hall, NJ, 1977. [3] D.H. Ballard, Parameter Nets, Artificial Intelligence, 22 (1984), 235-267. [4] D.H. Ballard and C.M. Brown, Computer Vision, Prentice Hall, NJ, 1982. [5] B.G. Batchelor, Pattern Recognition, Plenum Press, NY, 1978. [6] F.W. Campbell and J.G. Robson, Application of Fourier analysis to the visibility of gratings, J. Physiol., 197 (1968), 551-566. [7] O. Christensen and D.T. Stoeva, p-frames in separable Banach spaces, Advances in Computational Mathematics, 18 (2003), 117-126. [8] C. Chui (Editor), An Introduction to Wavelets, Volume 1, Academic Press Inc., NY, 1992. [9] C. Chui (Editor), A Tutorial in Theory and Application, Academic Press Inc., NY, 1992. [10] I. Daubechies, The wavelet transform, time frequency localization and signal analysis, IEEE Transactions on Information Theory, 36 (1990), no. 5, 961-1005. [11] I. Daubechies, Ten Lectures on Wavelets, Society for Industrial and Applied Mathematics, PA, 1992. [12] L. Debnath, Wavelet Transforms and their Applications, Birkh¨auser, MA, 2002. [13] R.C. Gonzalez and R. Woods, Digital Image Processing, Addison-Wesley Pub. Co., MA, 1992. [14] C.E. Heil and D.F. Walnut, Continuous and discrete wavelet transforms, Siam Review, 31 (1989), no. 4, 628-666. [15] B.B. Hubbard, The World According to Wavelets, A.K. Peters, MA, 1996. [16] A.K. Jain, Fundamentals of Digital Image Processing, Prentice Hall, NJ, 1989. [17] T.H. Koornwinder, Wavelets: An Elementary Treatment of Theory and Applications, World Scientific, NJ, 1993. [18] J.S. Lim, Two-Dimensional Signal and Image Processing, Prentice Hall, NJ, 1990. [19] S. Mallat and S. Zhong, Characterization of signals from multiscale edges, IEEE Transactions on Pattern Analysis and Machine Intelligence, 14 (1992), no. 7, 710-732. [20] Y. Meyer, Wavelet Algorithms and Application, SIAM (Translated by R. Ryan), PA, 1993. [21] G. Nagy, State of the art in pattern recognition, Proc. IEEE, 56 (1968), 836-862. [22] W. Pedrycz, Fuzzy sets in pattern recognition; methodology and methods, Pattern Recognition, 20 (1990), no. 1-2, 121-146. [23] W.K. Pratt, Digital Image Processing, John Wiley and Sons, NY, 1991. [24] M. Ruskai, G. Beylkin, R. Coifman, I. Daubechies, S. Mallat, Y. Meyer, and I. Raphael (Editors), Wavelets and their Applications, Jones and Bartlett, MA, 1992. [25] R.J. Schalkoff, Digital Image Processing and Computer Vision, John Wiley and Sons, NY, 1989. [26] J. Schmeelk, Wavelet transforms not Fourier transforms on two-dimensional images, International Journal of Computational and Numerical Analysis and Applications, 4 (2003), no. 2, 131-155. [27] G. Strange, Wavelet transforms versus Fourier transforms, Bulletin of the AMS, 28 (1993), no. 2, 288-305. [28] Y.Y. Tang, L.H. Yang, J. Liu, and H. Ma, Wavelet Theory and its Application to Pattern Recognition, World Scientific, NJ, 2000. [29] D.F. Walnut, An Introduction to Wavelet Analysis, Birkh¨auser, MA, 2002.