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Image processing with nonseparable multiwavelets
Keywords:
multiwavelets, nonseparable, quineunxAbstract
In a general context we introduce image processing with 1-dimensional wavelets and show the diferences with nonseparable 2-dimensional wavelets having quincunx decimation, in the first place, and with balanced nonseparable 2-dimensional multiwavelets, in the second place. All of them are orthogonal. Formulae for analysis and synthesis are given for the latter. The first steps are illustrated with images. The decomposition of the original image into 2 input images is explained. We illustrate with examples 2 applications: zoom-in (interpolation) and compression of images.
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References
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[8] A. Ruedin. Balanced nonseparable orthogonal multiwavelets with 2 and 3 vanishing moments on the quincunx grid. Proceedings SPIE Wavelet Appl. Signal Image Proc. VIII, 4119:to appear, 2000.
[9] V. Strela, P. Heller, G. Strang, P.Topiwala, and C. Heil. The application of multiwavelet lterbanks to signal and image processing. IEEE Transactions in Image Processing, to appear.
[10] V. Strela. Multiwavelets: Theory and Applications. PhD thesis, 1996.
[2] I. Daubechies. Ten lectures on wavelets.Society for Industrial and Appl Mathematics, 1992.
[3] J. Kovacevic and M. Vetterli. New results on multidi-mensional lter banks and wavelets. preprint.
[4] J. Kovacevic and M. Vetterli. Nonseparable multidimensional perfect reconstruction lter banks and wavelet bases forrn. IEEE, Transactions on Information Theory, 38(2):533{555, 1992.
[5] J. Lebrun and M. Vetterli. Balanced multiwavelets: Theory and design. IEEE Transactions on Signal Processing, 1997.
[6] G. Plonka and V.Strela. Construction of multiscaling functions with approximation and symmetry . SIAM Journal of Mathematical Analysis, 29:481-510, 1998.
[7] A. Ruedin. Nonseparable orthogonal multiwavelets with 2 and 3 vanishing moments on the quincunx grid. Proceedings SPIE Wavelet Appl. Signal Image Proc.
VII, 3813:455{466, 1999.
[8] A. Ruedin. Balanced nonseparable orthogonal multiwavelets with 2 and 3 vanishing moments on the quincunx grid. Proceedings SPIE Wavelet Appl. Signal Image Proc. VIII, 4119:to appear, 2000.
[9] V. Strela, P. Heller, G. Strang, P.Topiwala, and C. Heil. The application of multiwavelet lterbanks to signal and image processing. IEEE Transactions in Image Processing, to appear.
[10] V. Strela. Multiwavelets: Theory and Applications. PhD thesis, 1996.
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Published
2001-05-01
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[1]
“Image processing with nonseparable multiwavelets”, JCS&T, vol. 1, no. 04, p. 12 p., May 2001, Accessed: Mar. 08, 2026. [Online]. Available: https://journal.info.unlp.edu.ar/JCST/article/view/999
