TTHRESH: Tensor Compression for Multidimensional Visual Data

• Published in: IEEE transactions on visualization and computer graphics Vol. 26; no. 9; pp. 2891 - 2903
• Main Authors: Ballester-Ripoll, Rafael, Lindstrom, Peter, Pajarola, Renato
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.09.2020; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Archiving; Arithmetic coding; Compression algorithms; Data compression; Data visualization; Datasets; Encoding; higher-order singular value decomposition; Mathematical analysis; MATHEMATICS AND COMPUTING; Matrix decomposition; Multidimensional data; scientific visualization; Singular value decomposition; tensor decompositions; Tensors; Three-dimensional displays; Transform-based compression; Transforms; Tucker model; Visualization
• ISSN: 1077-2626; 1941-0506; 1941-0506
• DOI: 10.1109/TVCG.2019.2904063

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.