Tight Wavelet Frame Decomposition and Its Application in Image Processing

Mahmud Yunus (1Analysis and Geometry Group, FMIPA ITB, Bandung 2Department of Mathematics, FMIPA ITS, Surabaya)
Hendra Gunawan (1Analysis and Geometry Group, FMIPA ITB, Bandung)

Journal of Mathematical and Fundamental Sciences
Vol. 40 No. 2 (2008)

This paper is devoted to the formulation of a decomposition algorithm using tight wavelet frames, in a multivariate setting. We provide an alternative method for decomposing multivariate functions without accomplishing any tensor product. Furthermore, we give explicit examples of its application in image processing, particularly in edge detection and image denoising. Based on our numerical experiment, we show that the edge detection and the image denoising methods exploiting tight wavelet frame decomposition give better results compare with the other methods provided by MATLAB Image Processing Toolbox and classical wavelet methods.