Minimum-Energy Multiwavelet Frames with Arbitrary Integer Dilation Factor

Minimum-Energy Bivariate Wavelet Frame with Arbitrary Dilation Matrix

In order to characterize the bivariate signals, minimum-energy bivariate wavelet frames with arbitrary dilation matrix are studied, which are based on superiority of theminimum-energy frame and the significant properties of bivariate wavelet. Firstly, the concept ofminimum-energy bivariate wavelet frame is defined, and its equivalent characterizations and a necessary condition are presented. Se...

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...

Dual multiwavelet frames with symmetry from two-direction renable functions

Multiwavelet Frames from Refinable Function Vectors

Starting from any two compactly supported d-refinable function vectors in ( L2(R) )r with multiplicity r and dilation factor d, we show that it is always possible to construct 2rd wavelet functions with compact support such that they generate a pair of dual d-wavelet frames in L2(R) and they achieve the best possible orders of vanishing moments. When all the components of the two real-valued d-...

Orthogonal Multiwavelet Frames in L 2 Rd

We characterize the orthogonal frames and orthogonal multiwavelet frames in L2 R with matrix dilations of the form Df x √ |detA|f Ax , where A is an arbitrary expanding d × d matrix with integer coefficients. Firstly, through two arbitrarily multiwavelet frames, we give a simple construction of a pair of orthogonal multiwavelet frames. Then, by using the unitary extension principle, we present ...