The berization of aane systems via dual Gramian techniques, that was developed in previous papers of the authors, is applied here for the study of aane frames which have an aane dual system. Gramian techniques are also used to verify whether a dual pair of aane frames is a also a pair of bi-orthogonal Riesz bases. A general method for a painless derivation of a dual pair of aane frames from an ...

In this research, we study why prefiltering is necessary for discrete multiwavelet transforms. We propose a method to generate prefilters given a set of multiwavelet filterbanks, where they are called good prefitters.

Compactly supported Riesz wavelets are of interest in several applications such as image processing, computer graphics and numerical algorithms. In this paper, we shall investigate compactly supported MRA Riesz multiwavelet bases in L2(R). An algorithm is presented to derive Riesz multiwavelet bases from refinable function vectors. To illustrate our algorithm and results in this paper, we prese...

in this paper we introduce and study besselian $g$-frames. we show that the kernel of associated synthesis operator for a besselian $g$-frame is finite dimensional. we also introduce $alpha$-dual of a $g$-frame and we get some results when we use the hilbert-schmidt norm for the members of a $g$-frame in a finite dimensional hilbert space.

Multiwavelet has some important properties such as orthogonality, symmetry, and short support, which make up for the shortcoming of scalar wavelet. In this paper, we consider the problem of improving the performance of multiwavelet-based image coders combining human visual syetem (HVS). By taking into account the imperfections inherent to the HVS, HVS weighting is designed to achieve higher com...

Progressive collapse is a condition where local failure of a primary structural component leads to the collapse of neighboring members and the whole structure, consequently. In this paper, the progressive collapse potential of seismically designed steel dual systems with buckling restrained braces is investigated using the alternate path method, and their performances are compared with those of...

The demountable disk-drum aero-engine rotor is an important piece of equipment that greatly impacts the safe operation of aircraft. However, assembly looseness or crack fault has led to several unscheduled breakdowns and serious accidents. Thus, condition monitoring and fault diagnosis technique are required for identifying abnormal conditions. Customized ensemble multiwavelet method for aero-e...

A characterization of multivariate dual wavelet tight frames for any general dilation matrix is presented in this paper. As an application, Lawton’s result on wavelet tight frames in L(IR) is generalized to the n-dimensional case. Two ways of constructing certain dual wavelet tight frames in L(IR) are suggested. Finally examples of smooth wavelet tight frames in L(IR) and H(IR) are provided. In...

This paper investigates the emerging notion of multiwavelets in the context of multirate filter banks, and applies a multiwavelet system to image coding. Multiwavelets are of interest because their constituent filters can be simultaneously symmetric and orthogonal (this combination is impossible for 2-band PR-QMFs), and because one can obtain higher orders of approximation (more vanishing wavel...