  Memory and network bandwidth are decisive bottlenecks when handling
high-resolution multidimensional data sets in visualization applications, and
they increasingly demand suitable data compression strategies. We introduce a
novel lossy compression algorithm for multidimensional data over regular grids.
It leverages the higher-order singular value decomposition (HOSVD), a
generalization of the SVD to three dimensions and higher, together with
bit-plane, run-length and arithmetic coding to compress the HOSVD transform
coefficients. Our scheme degrades the data particularly smoothly and achieves
lower mean squared error than other state-of-the-art algorithms at
low-to-medium bit rates, as it is required in data archiving and management for
visualization purposes. Further advantages of the proposed algorithm include
very fine bit rate selection granularity and the ability to manipulate data at
very small cost in the compression domain, for example to reconstruct filtered
and/or subsampled versions of all (or selected parts) of the data set.
