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

TL;DR

Structured 3D-SVD offers an efficient framework for biological volumetric data compression and reconstruction, achieving high accuracy with reduced computation time and enabling progressive detail enhancement.

Contribution

It introduces a novel 3D-SVD based method inspired by matrix SVD for volumetric data, improving on existing tensor decompositions in accuracy and efficiency.

Findings

Achieves reconstruction quality close to Tucker decomposition.

Outperforms CPD in accuracy and runtime.

Low truncation levels preserve main structures effectively.

Abstract

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.