A Construction of a Pairwise Orthogonal Wavelet Frames Using Polyphase Matrix

Symmetry Feature and Construction for the 3-Band Tight Framelets with Prescribed Properties

A construction approach for the 3-band tight wavelet frames by factorization of paraunitarymatrix is developed. Several necessary constraints on the filter lengths and symmetric features of wavelet frames are investigated starting at the constructed paraunitary matrix. The matrix is a symmetric extension of the polyphase matrix corresponding to 3-band tight wavelet frames. Further, the paramete...

Minimum-energy wavelet frames generated by the Walsh polynomials

Abstract: Drawing inspiration from the construction of tight wavelet frames generated by the Walsh polynomials, we introduce the notion of minimum-energy wavelet frames generated by the Walsh polynomials on positive half-line R using unitary extension principles and present its equivalent characterizations in terms of their framelet symbols. Moreover, based on polyphase components of the Walsh ...

Wavelets, multiwavelets and wavelet frames for periodic functions

Various results on constructing wavelets, multiwavelets and wavelet frames for periodic functions are reviewed. The orthonormal and Riesz bases as well as frames are constructed from sequences of subspaces called multiresolution analyses. These studies employ general frequency-based approaches facilitated by functions known as orthogonal splines and polyphase splines. While the focus is on the ...

Construction of Compactly Supported Nonseparable Orthogonal Wavelets of L^2(R^n)

Scaling Laplacian Pyramids

Laplacian pyramid based Laurent polynomial (LP2) matrices are generated by Laurent polynomial column vectors and have long been studied in connection with Laplacian pyramidal algorithms in Signal Processing. In this paper, we investigate when such matrices are scalable, that is when right multiplication by Laurent polynomial diagonal matrices results in paraunitary matrices. The notion of scala...