The Characterization of Orthogonal Affine Bivariate Pseudoframes
The frame theory has been one of powerful tools for researching into wavelets. The notion of the bivariate generalized multiresolution structure (BGMS) is presented. The concepts of Bessel sequences and orthogonal bivariate pseudoframes are introduced. Two Bessel sequences are said to be orthogonal ones if the composition of synthesis operator of one sequence with the analysis operator of the other is the zero-operator. It is characterized that when two Bessel sequences are orthogonal while the Bessel sequences possess the form of translates of a finite number of bivariate functions in . A constructive method for affine frames of based on a BGMS is established.
Xie Yi and Li Mi
Q. J. Chen and F. Lin, "The Characterization of Orthogonal Affine Bivariate Pseudoframes", Advanced Materials Research, Vols. 129-131, pp. 33-37, 2010