Symmetric tight frame wavelets with dilation factor M=4

Construction of symmetric orthogonal bases of wavelets and tight wavelet frames with integer dilation factor

Our goal is to present a systematic algorithm for constructing (anti)symmetric tight wavelet frames and orthonormal wavelet bases generated by a given refinable function with an integer dilation factor d 2. Special attention is paid to the issues of the minimality of a number of framelet generators and the size of generator supports. In particular, our algorithm allows to reduce the computation...

Symmetric orthonormal scaling functions and wavelets with dilation factor 4

It is well known that in the univariate case, up to an integer shift and possible sign change, there is no dyadic compactly supported symmetric orthonormal scaling function except for the Haar function. In this paper we are concerned with the construction of symmetric orthonormal scaling functions with dilation factor d = 4. Several examples of such scaling functions are provided in this paper....

Tight frame wavelets and the dimension function

Minimally Supported Frequency Composite Dilation Parseval Frame Wavelets

Abstract. A composite dilation Parseval frame wavelet is a collection of functions generating a Parseval frame for L2(Rn) under the actions of translations from a full rank lattice and dilations by products of elements of groups A and B. A minimally supported frequency composite dilation Parseval frame wavelet has generating functions whose Fourier transforms are characteristic functions of set...

Connectivity in the set of Tight Frame Wavelets (TFW)

We introduce new ideas to treat the problem of connectivity of wavelets. We develop a method which produces intermediate paths of Tight Frame Wavelets (TFW). Using this method we prove that a large class of TFW-s, with only mild conditions on their spectrum, are arcwise connected.