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

In this paper, we study minimum-energy frame Ψ = { ψ 1 , ψ 2 , … , ψ M } on the interval with arbitrary factor d for L 2 [ 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 L 2 [ 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.