The paper shows that there exist wavelet frames generated by two functions which have good dual wavelet frames,but for which the standard dual wavelet frame does not consist of wavelets,namely,the standard dual wavelet frame cannot be generated by the translations and dilations of a single function.

The concept of dual frame of subspace frame was generalized.

It introduces the concept of dual frame of Banach frame,dual frame of frame of order p,and pair of dual frames.

Introduced the concepts of dual frame for q-frame and q-Riesz frame in Banach spaces.

It introduces the concept of dual frame of Banach frame,dual frame of frame of order p,and pair of dual frames.

To large-dimensional wavelet networks based on single scaling wavelet frames theory, a systematic design method is proposed.

A set of wavelet frames generated by Gaussian radial basis functions are presented.

A new method based on discriminative wavelet frames is proposed for the classification of textile defects.

Digital wavelet frame denoise the transient scatter response signals;

The localization theorem of wavelet frame expansion formula in strip of Sobolev spaces is established,such that a localization theorem of wavelet frame expansion in L 2(R) is only a particular example of this theorem when S =0.

Based on wavelet frame theory, a new principle of transient protection is proposed, which applies the energy mutation of non unit transient current to detect the occurrence of fault as the actuating component of protection.

In this paper,we study semi-orthogonal frame wavelets(PFWs) in L2(Rd) with A dilations,where A is an arbitrary expanding d×d matrix,such that│det A│= c,c∈N.

For a pair of dual frame multiresolution analyses,we construct a pair of dual frame wavelets and a pair of quasi-biorthogonal frame wavelets with the help of filter banks.