Algorithm 5 Customized Wavelet Base Initialization (CWBI)

${\mathcal{T}}_b\leftarrow ({\mathbf{y}}_b,{\mathbf{P}}_{-1},{\stackrel{‒}{\mathbf{w}}}_{-1})$; use Algorithm 2 to calculate the suboptimal transformation ${\mathcal{T}}_b$ of (26) without shape constraints.

${\tilde{\mathbf{x}}}_b\leftarrow {\mathcal{T}}_b^{-1}\left(S_b\right)$

${\mathbf{w}}_{-1,b}\leftarrow {\tilde{\mathbf{x}}}_b$; define a new scaling coefficients w−1,b at the coarsest scale based on the assumption of (28) and set it equal to ${\tilde{\mathbf{x}}}_b$.

$\mathbf{x}\leftarrow {\mathcal{W}}^{-1}({\mathbf{w}}_{-1,b}\cup \{{\stackrel{‒}{\mathbf{w}}}_l,l\ge 0\left\}\right)$

${\tilde{\mathbf{y}}}^{\left(0\right)}\leftarrow {\mathcal{T}}_b\left(\mathbf{x}\right)$