The Constructing Theory Of Armlets Multiwavelets And Shearlets

In recent years, multiwavelet theory is being rapidly developed and extremely impor-tant area of research topic in wavelet theory, Armlets multiwavelet is a research hotspot recently. Since wavelet and multiwavlet couldn’t effectively provide the direction informa-tion of signal, but shearlet could provide more direction information of signal than wavelet and multiwavelet, so shearlet is a research hotspot in directional representation system.Based on the former work, we study Armlets multiwavelets and shearlet in this paper. Our main results in following threefold:In section 2, we give a sufficient and necessary condition for the relation between the decomposition of the matrix symbol of Armlets multiwavelets and Armlets multiwavelets with multiplicity r and dilation a. We show three examples to verify our conclusion.In section 3, we construct a transformation matrix M, then, we show the explicit con-struction of Armlets multiwavelets with multiplicity 4 by using non-Armlets multiwavelets with multiplicity 4, this construction is based on the former work. We show an example to verify our conclusion.In section 4, we show three lemmas for continuous shearlet transform, then we obtain Heisenberg uncertainty principle for continuous shearlet transform, finally, we generalize this result to three different types.