Minimum-Energy Multiwavelet Frames with Arbitrary Integer Dilation Factor

Abstract EN

In order to organically combine the minimum-energy frame with the significant properties of multiwavelets, minimum-energy multiwavelet frames with arbitrary integer dilation factor are studied.

Firstly, we define the concept of minimum-energy multiwavelet frame with arbitrary dilation factor and present its equivalent characterizations.

Secondly, some necessary conditions and sufficient conditions for minimum-energy multiwavelet frame are given.

Thirdly, the decomposition and reconstruction formulas of minimum-energy multiwavelet frame with arbitrary integer dilation factor are deduced.

Finally, we give several numerical examples based on B-spline functions.