Non-separable wavelet

<p>Non-separable wavelets are multi-dimensional <a href="/facts/Wavelet/3XcX4uIP">wavelets</a> that are not directly implemented as <a href="/facts/Tensor_product/7K3pR1ap">tensor products</a> of wavelets on some lower-dimensional space.
They have been studied since 1992.
They offer a few important advantages. Notably, using non-separable filters leads to more parameters in design, and consequently better filters.
The main difference, when compared to the one-dimensional wavelets, is that <a href="/facts/Multidimensional_sampling/10UJv920">multi-dimensional sampling</a> requires the use of <a href="/facts/Lattice_(group)/2ls9Iv9N">lattices</a> (e.g., the quincunx lattice).
The wavelet filters themselves can be separable or non-separable regardless of the sampling lattice.
Thus, in some cases, the non-separable wavelets can be implemented in a separable fashion.
Unlike separable wavelet, the non-separable wavelets are capable of detecting structures that are not only horizontal, vertical or diagonal (show less <a href="/facts/Anisotropy/YMqTQWVB">anisotropy</a>).
</p>

Non-separable wavelet open-in-new

Non-separable wavelet