TTHRESH: Tensor Compression for Multidimensional Visual Data

TL;DR

This paper presents TTHRESH, a novel lossy compression algorithm for multidimensional data that leverages HOSVD and advanced coding techniques to achieve smooth data degradation and lower error at low-to-medium bit rates, suitable for visualization.

Contribution

It introduces a new tensor-based compression method combining HOSVD with bit-plane and entropy coding, enabling fine bit rate control and efficient data manipulation in the compression domain.

Findings

Achieves lower mean squared error than state-of-the-art algorithms at low-to-medium bit rates.

Allows fine granularity in bit rate selection for better data control.

Enables manipulation of data within the compression domain with minimal computational cost.

Abstract

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.