Minimum-energy frames associated with refinable function of arbitrary integer dilation factor

作者：Huang Yongdong^*; Cheng Zhengxing

来源：Chaos Solitons & Fractals, 2007, 32(2): 503-515.

DOI：10.1016/j.chaos.2006.06.082

In this paper, we study minimum-energy frame psi = {psi(1), psi(2),...,psi(N)} with arbitrary integer dilation factor d for L-2(R), psi correspond to some refinable functions with compact support. A precise existence criterion of psi is given in terms of an inequality condition on the Laurent polynomial symbols of the refinable functions. We give a constructive proof that when psi does exist, d functions with compact support are sufficient to constitute psi, and present a explicit formula of constructing psi. Finally, we present the minimum-energy frames decomposition and reconstruction formulas which are similar to those of orthogonal wavelets. Numerical examples are given.

• 出版日期2007-4
• 单位西安交通大学