The Excellent Traits of a Class of Orthogonal Quarternary Wavelet Wraps with Short Support
The frame theory has been one of powerful tools for researching into wavelets. In this article, the notion of orthogonal nonseparable quarternary wavelet wraps, which is the generalizati- -on of orthogonal univariate wavelet wraps, is presented. A novel approach for constructing them is presented by iteration method and functional analysis method. A liable approach for constructing two-directional orthogonal wavelet wraps is developed. The orthogonality property of quarternary wavelet wraps is discussed. Three orthogonality formulas concerning these wavelet wraps are estabished. A constructive method for affine frames of L2(R4) is proposed. 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 multiresolution structure.
Helen Zhang, Gang Shen and David Jin
G. X. Wang and D. L. Hua, "The Excellent Traits of a Class of Orthogonal Quarternary Wavelet Wraps with Short Support", Advanced Materials Research, Vols. 219-220, pp. 496-499, 2011