The Research of Bivariate Minimum-Energy Wavelet Frames and Pseudoframes
Frames have become the focus of active research, both in theory and in applications. In the article, the notion of bivariate minimum-energy wavelet frames is introduced. A precise existence criterion for minimum-energy frames in terms of an inequality condition on the Laurent polynomial symbols of the filter functions is provided. An explicit formula for designing minimum-energy frames is also establish- ed. The sufficient condition for the existence of a class of affine pseudoframes with filter banks is obtained by virtue of a generalized multiresolution analysis. The pyramid decomposition scheme is established based on such a generalized multiresol- -ution structure.
P. A. Wang "The Research of Bivariate Minimum-Energy Wavelet Frames and Pseudoframes", Advanced Materials Research, Vol. 159, pp. 1-6, 2011