Differentiable wavelet family for $L^2(\mathbb{R}^d)$?

Question

A family of functions $\psi^{1}, ..., \psi^M \in L^2(\mathbb{R}^d)$ is called a wavelet-family if \begin{equation} \left\{\psi^i_{j,k}(x) = 2^{\frac{vj}{2}} \psi^i\left(2^jx - k \right) \middle| j \in \mathbb{Z}, k \in \mathbb{Z}^n, i = 1, ..., M \right\} \end{equation} is an orthonormal basis for $\mathbb{R}^v$. This basis is called a wavelet base (cp. 1 ). I need such a wavelet-base, such that $\psi^i$ is twice continuously differentiable. Unfortunately I cannot find any concrete hint on this problem in the literature.