A tensor-product wavelet is a product of one-dimensional <wavelets> and <scaling functions>, with at least one wavelet factor. In two dimensions, the three simultaneous-scale types are $\psi\otimes\varphi$, $\varphi\otimes\psi$ and $\psi\otimes\psi$. Their translates and normalized dilates form a <tensor-product wavelet basis>.


Tensor-product wavelet

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.


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 Incoming links: Tensor-product wavelet basis