On the higher-dimensional wavelet frames

AbstractEvery higher-dimensional wavelet frame is generated by dyadic dilations and integer translates of several mother functions. In this paper, associated with a frame multiresolution analysis {Vm,ϕ} of L2(Rd), many higher-dimensional wavelet frames are constructed with help of a splitting trick of the subspace V1 and a very fine partition of Rd. The least number of the mother functions is shown precisely in terms of the index of the FMRA. Finally, in order to explain our theory, an example is presented