Research on Minimum-energy Interval Vector-valued Frame

This paper discusses the construction of the minimum-energy vector-valued frame generated by the wavelets with arbitrary integer dilation factor d on the interval [0, 1], associated with some vector-valued refinable functions of compact support. We first give the construction method of the minimum-energy interval vector-valued frames associate with vector-valued refinable functions of any integer support, and then get the equivalent statements with respect to existence of the interval vector-valued frames. Finally, we present the algorithms about the minimum-energy interval vector-valued frame decomposition and reconstruction.