# TTHRESH: Tensor Compression for Multidimensional Visual Data

arXiv: https://arxiv.org/abs/1806.05952 · HTML: https://mlsanity.com/paper/1806.05952/

## Key facts

- Cited by 42 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jun 2018.

## Built on by (most cited first, 30 of 42)

- [Compressive Neural Representations of Volumetric Scalar Fields](https://mlsanity.com/paper/2104.04523/) (2021)
- [Tensor Methods in Computer Vision and Deep Learning](https://mlsanity.com/paper/2107.03436/) (2021)
- [Fast Neural Representations for Direct Volume Rendering](https://mlsanity.com/paper/2112.01579/) (2021)
- [Tensor Networks Meet Neural Networks: A Survey and Future Perspectives](https://mlsanity.com/paper/2302.09019/) (2023)
- [Compressing multidimensional weather and climate data into neural networks](https://mlsanity.com/paper/2210.12538/) (2022)
- [Interactive Volume Visualization via Multi-Resolution Hash Encoding based Neural Representation](https://mlsanity.com/paper/2207.11620/) (2022)
- [ECNR: Efficient Compressive Neural Representation of Time-Varying Volumetric Datasets](https://mlsanity.com/paper/2311.12831/) (2023)
- [Adaptively Placed Multi-Grid Scene Representation Networks for Large-Scale Data Visualization](https://mlsanity.com/paper/2308.02494/) (2023)
- [Deep Hierarchical Super Resolution for Scientific Data](https://mlsanity.com/paper/2107.00462/) (2021)
- [Lossy Neural Compression for Geospatial Analytics: A Review](https://mlsanity.com/paper/2503.01505/) (2025)
- [Distributed Neural Representation for Reactive in situ Visualization](https://mlsanity.com/paper/2304.10516/) (2023)
- [MGARD: A multigrid framework for high-performance, error-controlled data compression and refactoring](https://mlsanity.com/paper/2401.05994/) (2024)
- [TT-NF: Tensor Train Neural Fields](https://mlsanity.com/paper/2209.15529/) (2022)
- [SRN-SZ: Deep Leaning-Based Scientific Error-bounded Lossy Compression with Super-resolution Neural Networks](https://mlsanity.com/paper/2309.04037/) (2023)
- [Accelerating Communication in Deep Learning Recommendation Model Training with Dual-Level Adaptive Lossy Compression](https://mlsanity.com/paper/2407.04272/) (2024)
- [Attention Based Machine Learning Methods for Data Reduction with Guaranteed Error Bounds](https://mlsanity.com/paper/2409.05357/) (2024)
- [Cherry-Picking Gradients: Learning Low-Rank Embeddings of Visual Data via Differentiable Cross-Approximation](https://mlsanity.com/paper/2105.14250/) (2021)
- [Neural Fields for Interactive Visualization of Statistical Dependencies in 3D Simulation Ensembles](https://mlsanity.com/paper/2307.02203/) (2023)
- [Efficient Neural Representation of Volumetric Data using Coordinate-Based Networks](https://mlsanity.com/paper/2401.08840/) (2024)
- [NeurLZ: An Online Neural Learning-Based Method to Enhance Scientific Lossy Compression](https://mlsanity.com/paper/2409.05785/) (2024)
- [F-Hash: Feature-Based Hash Design for Time-Varying Volume Visualization via Multi-Resolution Tesseract Encoding](https://mlsanity.com/paper/2507.03836/) (2025)
- [Protecting Big Data Privacy Using Randomized Tensor Network Decomposition and Dispersed Tensor Computation](https://mlsanity.com/paper/2101.04194/) (2021)
- [T4DT: Tensorizing Time for Learning Temporal 3D Visual Data](https://mlsanity.com/paper/2208.01421/) (2022)
- [Machine Learning Techniques for Data Reduction of CFD Applications](https://mlsanity.com/paper/2404.18063/) (2024)
- [Generative Latent Diffusion for Efficient Spatiotemporal Data Reduction](https://mlsanity.com/paper/2507.02129/) (2025)
- [ANTIC: Adaptive Neural Temporal In-situ Compressor](https://mlsanity.com/paper/2604.09543/) (2026)
- [Tensor-Tensor Products, Group Representations, and Semidefinite Programming](https://mlsanity.com/paper/2507.12729/) (2025)
- [REV-INR: Regularized Evidential Implicit Neural Representation for Uncertainty-Aware Volume Visualization](https://mlsanity.com/paper/2601.17689/) (2026)
- [GaussianPile: A Unified Sparse Gaussian Splatting Framework for Slice-based Volumetric Reconstruction](https://mlsanity.com/paper/2603.20611/) (2026)
- [A Geometric Lens on Physics-Aligned Data Compression](https://mlsanity.com/paper/2606.03279/) (2026)

## Abstract (arXiv)

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.