Minimum-energy wavelet frame on the interval with arbitrary integer dilation factor

AbstractIn this paper, we study minimum-energy frame Ψ={ψ1,ψ2,…,ψM} on the interval with arbitrary factor d for L2[0,1], Ψ corresponding to some refinable functions with compact support. We give the constructive proof as well as the necessary and sufficient conditions of minimum-energy frames for L2[0,1], present the decomposition and reconstruction formulas of minimum-energy frame on the interval [0,1], and some examples. The experimental results show that the proposed minimum-energy frame on the interval improves the performance in the application of image denoising significantly

Minimum-Energy Bivariate Wavelet Frame with Arbitrary Dilation Matrix

In order to characterize the bivariate signals, minimum-energy bivariate wavelet frames with arbitrary dilation matrix are studied, which are based on superiority of the minimum-energy frame and the significant properties of bivariate wavelet. Firstly, the concept of minimum-energy bivariate wavelet frame is defined, and its equivalent characterizations and a necessary condition are presented. Secondly, based on polyphase form of symbol functions of scaling function and wavelet function, two sufficient conditions and an explicit constructed method are given. Finally, the decomposition algorithm, reconstruction algorithm, and numerical examples are designed