Symmetric Mra Tight Wavelet Frames with Three Generators and High Vanishing Moments

Let φ be a compactly supported symmetric real-valued refinable function in L2(R) with a finitely supported symmetric real-valued mask on Z. Under the assumption that the shifts of φ are stable, in this paper we prove that one can always construct three wavelet functions ψ, ψ and ψ such that (i) All the wavelet functions ψ, ψ and ψ are compactly supported, real-valued and finite linear combinations of the functions φ(2 · −k), k ∈ Z; (ii) Each of the wavelet functions ψ, ψ and ψ is either symmetric or antisymmetric; (iii) {ψ1, ψ, ψ3} generates a tight wavelet frame in L2(R), that is, ‖f‖2 = 3 ∑