DWTn
DWTn, short for discrete wavelet transform in n dimensions, is a family of multi-dimensional signal representations that generalizes the conventional one-dimensional discrete wavelet transform to data sets defined in any number of dimensions. Like the standard DWT, DWTn decomposes a signal into approximation and detail components at successive scales, enabling multiresolution analysis and efficient data sparsification. In practice, DWTn is implemented via separable filter banks along each dimension or via non-separable, cross-dimensional wavelets for more complex correlations.
In separable implementations, a 1D wavelet filter pair is applied along each axis in sequence, producing a
Applications include image and video compression, denoising, medical imaging, geophysical data analysis, and scientific visualization, where
Key considerations when using DWTn include choice of mother wavelet, boundary handling for finite-sized data, and