# Structured 3D-SVD: A Practical Framework for the Compression and Reconstruction of Biological Volumetric Images

arXiv: https://arxiv.org/abs/2604.16947 · HTML: https://mlsanity.com/paper/2604.16947/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 21 references that are in the map.
- First posted on arXiv 18 Apr 2026.

## Builds on (most cited first, 3 of 3)

- [Towards Quantum Tensor Decomposition in Biomedical Applications](https://mlsanity.com/paper/2502.13140/) (2025)
- [Compression of volume-surface integral equation matrices via Tucker decomposition for magnetic resonance applications](https://mlsanity.com/paper/2103.06393/) (2021)
- [Tensorial tomographic differential phase-contrast microscopy](https://mlsanity.com/paper/2204.11397/) (2022)

## Abstract (arXiv)

This work introduces Structured 3D-SVD as a practical framework for the reconstruction, compression, and analysis of biological volumetric data. Inspired by the logic of matrix singular value decomposition (SVD), the proposed approach represents third-order volumetric data in the spatial domain and supports progressive reconstruction through ordered quasi-singular coeffients. The experimental evaluation was carried out on two biological volumetric datasets: one full-volume scan of a fish and another of a brain. The results show that Structured 3D-SVD achieves reconstruction quality close to that of Tucker decomposition while requiring shorter computation times and outperforms canonical polyadic decomposition (CPD) in both accuracy and runtime. In addition, a progressive reconstruction analysis shows that relatively low truncation levels are sufficient to preserve the main volumetric structures, while higher truncation levels lead to more detailed reconstructions.