High dimensional data compression via PHLCT (with Z. Zhang),
Wavelets XII (D. Van De Ville, V. K. Goyal, and M. Papadakis, eds.), Proc. SPIE 6701, Paper #670127, 2007.
The polyharmonic local cosine transform (PHLCT), presented by Yamatani and Saito in 2006, is a new tool for local image analysis and synthesis. It can
compress and decompress images with better visual fidelity, less blocking
artifacts, and better PSNR than those processed by the JPEG-DCT algorithm.
Now, we generalize PHLCT to the high-dimensional case and apply it
to compress the high-dimensional data. For this purpose, we give the
solution of the high-dimensional Poisson equation with the Neumann
boundary condition. In order to reduce the number of coefficients of
PHLCT, we use not only d-dimensional PHLCT decomposition, but also
d-1, d-2, ..., 1 dimensional PHLCT decompositions. We find that our
algorithm can more efficiently compress the high-dimensional data than
the block DCT algorithm.
We will demonstrate our claim using both synthetic and real 3D datasets.
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