Tensor-product wavelet basis
= Tensor-product wavelet basis
From a one-dimensional <multiresolution analysis>, the simultaneous-scale two-dimensional detail space splits as $(W_j\otimes V_j)\oplus(V_j\otimes W_j)\oplus(W_j\otimes W_j)$. Its generating <wavelets> are $\psi\otimes\varphi$, $\varphi\otimes\psi$, and $\psi\otimes\psi$. Their normalized dilates are $2^j\Psi(2^j\cdot-k)$ for $k\in\mathbb Z^2$. Include a coarse scaling family when working on a bounded square.