TTHRESH: Tensor Compression for Multidimensional Visual Data

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 $N$-dimensional data over regular grids. It leverages the higher-order singular value decomposition (HOSVD), a generalization of the SVD to 3 and more dimensions, together with adaptive quantization, run-length and arithmetic coding to store the HOSVD transform coefficients' relative positions as sorted by their absolute magnitude. Our scheme degrades the data particularly smoothly and outperforms other state-of-the-art volume compressors at low-to-medium bit rates, as required in data archiving and management for visualization purposes. Further advantages of the proposed algorithm include extremely fine bit rate selection granularity, bounded resulting $l^2$ error, and the ability to manipulate data at very small cost in the compression domain, for example to reconstruct subsampled or filtered-resampled versions of all (or selected parts) of the data set.