Minimum-energy Multi-wavelets Tight Frames Associated With Two Scaling Functions

ABSTRACT:Multi-wavelets tight frames not only can hold the advantages of orthogonal wavelet but also can solve its disadvantages. At present, there are many important researches on multi-wavelets tight frames with one scaling function. But there are few conclusions about multi-wavelets tight frames which is associated with more than one scale functions. On the base of multi-wavelets and minimum-energy tight frames, we study minimum-energy multi-wavelets tight frames, and mainly consider about minimum-energy multi-wavelets tight frames associated with two compactly support scaling functions. We give an existence criterion for minimum-energy multi-wavelets tight frames. If the scaling functions of the minimum-energy multi-wavelets tight frames changed by an orthogonal matrix, the new scaling functions also can generate a minimum-energy multi-wavelets tight frame. Finally, we give two examples of minimum-energy multi-wavelets tight frames.