High-dimensional data compression via PHLCT

The polyharmonic local cosine transform (PHLCT), presented by Yamatani and Saito(1) 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.