Journal of Applied Mathematics
Volume 2013 (2013), Article ID 896050, 10 pages
Research Article

Minimum-Energy Bivariate Wavelet Frame with Arbitrary Dilation Matrix

School of Mathematics and Information Science, Beifang University of Nationalities, Yinchuan 750021, China

Received 31 January 2013; Revised 10 June 2013; Accepted 18 June 2013

Academic Editor: Li Weili

Copyright © 2013 Fengjuan Zhu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In order to characterize the bivariate signals, minimum-energy bivariate wavelet frames with arbitrary dilation matrix are studied, which are based on superiority of the minimum-energy frame and the significant properties of bivariate wavelet. Firstly, the concept of minimum-energy bivariate wavelet frame is defined, and its equivalent characterizations and a necessary condition are presented. Secondly, based on polyphase form of symbol functions of scaling function and wavelet function, two sufficient conditions and an explicit constructed method are given. Finally, the decomposition algorithm, reconstruction algorithm, and numerical examples are designed.