Efficient Multiresolution Transform

We exploit the theory of optimal sampling lattices in designing wavelets and filter banks for volumetric datasets. A true multidimensional (non-separable) wavelet transform is derived and applied to various datasets for comparison with the corresponding separable multidimensional method. We propose a non-separable wavelet transform that yields the subsampled data on an optimal sampling lattice. This new non-separable filter bank allows for more accurate and efficient multi-resolution representation of the data over the traditional separable transforms. Furthermore, we take advantage of methods that render the data directly from this optimal sampling lattice to get images that demonstrate the superior fidelity of the subsampled data of our new algorithm compared to traditional methods.