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

Antonio Le\'on; Mario Aragon\'es Lozano; Oscar Romero

arxiv: 2604.16947 · v1 · submitted 2026-04-18 · 📡 eess.IV · cs.CV· cs.NA· math.NA

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

Mario Aragon\'es Lozano , Oscar Romero , Antonio Le\'on This is my paper

Pith reviewed 2026-05-10 07:08 UTC · model grok-4.3

classification 📡 eess.IV cs.CVcs.NAmath.NA

keywords 3D image compressionvolumetric reconstructionSVDbiological imagingtensor decompositionprogressive reconstructionTucker decompositionCPD

0 comments

The pith

Structured 3D-SVD reconstructs biological volumetric images with quality close to Tucker decomposition but with shorter computation times and better performance than CPD.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper introduces Structured 3D-SVD as a framework for compressing and reconstructing third-order biological volume data by extending matrix SVD logic into the spatial domain. It represents the data using ordered quasi-singular coefficients that enable progressive reconstruction, starting from core structures and adding detail as needed. Experiments on full scans of a fish and a brain show reconstruction quality near that of Tucker decomposition while taking less time, and clear advantages over canonical polyadic decomposition in both accuracy and speed. Low levels of truncation already preserve the main volumetric features, suggesting the approach suits practical storage and analysis tasks where full detail is not always required immediately.

Core claim

Structured 3D-SVD represents third-order volumetric data through ordered quasi-singular coefficients in the spatial domain, supporting progressive reconstruction that achieves quality comparable to Tucker decomposition at reduced computational cost while outperforming canonical polyadic decomposition in both accuracy and runtime, as demonstrated on fish and brain biological datasets.

What carries the argument

The Structured 3D-SVD representation, which orders quasi-singular coefficients to allow progressive build-up of third-order tensor volumes from main features outward.

If this is right

Low truncation levels suffice to retain main structures, enabling quick low-detail previews before full reconstruction.
The method offers a speed-accuracy trade-off better than CPD for these biological volumes.
Compression becomes feasible while preserving progressive access to detail levels.
Analysis tasks can use the coefficient ordering to identify which features matter most at each scale.
Runtime savings compared to Tucker support repeated processing on large scan sets.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

If the coefficient ordering proves stable, the same structure could guide feature extraction in other volumetric imaging domains such as medical CT or microscopy.
The approach might reduce storage costs in research archives by allowing on-demand detail addition rather than full high-resolution files.
Extending the ordering rule to higher-order tensors could open compression paths for four-dimensional time-series volumes.
Integration with existing tensor toolkits would let users test the method directly on their own biological data without new code.

Load-bearing premise

The ordered quasi-singular coefficients capture essential features of biological volumes in a general way that holds across different samples without needing dataset-specific tuning.

What would settle it

Running Structured 3D-SVD on a new biological volume dataset where reconstruction quality falls below Tucker levels or requires per-sample retuning to match reported performance would show the method does not generalize as claimed.

Figures

Figures reproduced from arXiv: 2604.16947 by Antonio Le\'on, Mario Aragon\'es Lozano, Oscar Romero.

**Figure 3.** Figure 3: Accumulated PER as a function of the truncation level k for (a) the fish volumetric dataset and (b) the brain volumetric dataset [PITH_FULL_IMAGE:figures/full_fig_p015_3.png] view at source ↗

read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This is a practical but incremental 3D-SVD tweak for bio-volume compression that shows runtime gains on two scans yet leaves generality and implementation details unproven.

read the letter

The main thing here is a structured way to apply SVD-style decomposition to third-order volumetric data, using ordered quasi-singular coefficients to enable progressive reconstruction. That ordering is the piece that feels new relative to standard Tucker or CPD approaches, and the paper positions it as a direct, usable tool for biological imaging rather than a theoretical advance. On the two tested volumes (one fish scan, one brain scan) it reportedly matches Tucker quality with less compute time and beats CPD on both accuracy and speed, while low truncation levels already keep the main structures intact. That practical angle is where it earns its keep for labs dealing with large 3D datasets and storage costs. The soft spots are straightforward. Everything rests on just those two specific volumes, so we have no evidence yet that the coefficient ordering or the chosen structure transfers to other biological samples with different noise, resolution, or spatial statistics. The abstract gives no equations, no exact error metrics, no statistical tests, and no description of how the structure itself is defined or whether any choices were held fixed across datasets. If the ordering or truncation turns out to be tuned to these particular scans, the claimed advantages would not necessarily hold more broadly. The work is honest in what it attempts and the citation pattern looks clean, but the evidence is still thin for the generality it implies. This is the kind of paper that belongs in a methods-focused imaging journal or conference proceedings. A serious referee would be useful to press on the implementation details, the exact definition of the structure, and whether the performance edge survives on additional volumes. I would send it to review rather than desk-reject, with the expectation that the authors will need to add those checks and metrics.

Referee Report

3 major / 2 minor

Summary. The manuscript proposes Structured 3D-SVD, a framework extending matrix SVD logic to third-order volumetric biological data via a structured spatial-domain representation that supports progressive reconstruction using ordered quasi-singular coefficients. Experiments on two datasets (a full-volume fish scan and a brain scan) report that the method achieves reconstruction quality close to Tucker decomposition while requiring shorter computation times and outperforms canonical polyadic decomposition (CPD) in both accuracy and runtime; low truncation levels are shown to preserve main structures.

Significance. If the performance claims and generality hold, the approach offers a practical, computationally lighter alternative for compression and multi-resolution analysis of large biological volumes, with potential utility in imaging pipelines where Tucker-level quality is desired without full tensor decomposition cost. The progressive reconstruction feature is a clear strength for applications requiring scalable detail.

major comments (3)

[Experimental Evaluation] Experimental Evaluation section: The central performance claims rest on results from only two specific volumes (one fish scan, one brain scan). This limited scope does not adequately test whether the ordered quasi-singular coefficients and structured 3D representation capture essential features in a dataset-independent manner, as different biological samples may exhibit varying spatial statistics, noise, or resolution that could alter the observed advantages over Tucker and CPD.
[Method] Method section (definition of quasi-singular coefficients): The ordering mechanism and exact computation of the 'quasi-singular coefficients' must be formalized with explicit equations to confirm they extend SVD logic without introducing hidden dataset-dependent choices beyond the listed truncation levels. Absent this, reproducibility is compromised and it is unclear whether the claimed parameter-light nature holds.
[Results] Results section (quantitative comparisons): The assertions of 'close to Tucker' quality and outperforming CPD require tabulated metrics (e.g., PSNR/SSIM values, exact runtime figures) with clear baseline implementations and, ideally, statistical tests; qualitative statements alone are insufficient to substantiate the load-bearing claims about accuracy-runtime trade-offs.

minor comments (2)

[Abstract] Abstract: Typo in 'coeffients' (should be 'coefficients').
[References / Experiments] Ensure all tensor decomposition references (Tucker, CPD) include complete citations and that any implementation details (e.g., software libraries used for baselines) are stated for reproducibility.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the insightful comments, which have helped improve the clarity and rigor of our manuscript. We address each major comment below and indicate the revisions made.

read point-by-point responses

Referee: Experimental Evaluation section: The central performance claims rest on results from only two specific volumes (one fish scan, one brain scan). This limited scope does not adequately test whether the ordered quasi-singular coefficients and structured 3D representation capture essential features in a dataset-independent manner, as different biological samples may exhibit varying spatial statistics, noise, or resolution that could alter the observed advantages over Tucker and CPD.

Authors: We selected these two volumes as they represent distinct biological imaging scenarios with different structural complexities. The fish scan provides a large-scale anatomical view, while the brain scan offers higher-resolution neural details. Although we recognize that testing on additional datasets would strengthen claims of generality, the consistent performance trends observed support the method's applicability. In the revised version, we have expanded the discussion to address potential variations in spatial statistics across datasets and outlined plans for future validation on more diverse volumes. revision: partial
Referee: Method section (definition of quasi-singular coefficients): The ordering mechanism and exact computation of the 'quasi-singular coefficients' must be formalized with explicit equations to confirm they extend SVD logic without introducing hidden dataset-dependent choices beyond the listed truncation levels. Absent this, reproducibility is compromised and it is unclear whether the claimed parameter-light nature holds.

Authors: We appreciate this observation. The quasi-singular coefficients are computed by applying a structured decomposition in the spatial domain, with ordering based on their magnitudes to enable progressive reconstruction, analogous to singular values in SVD. To enhance reproducibility, we have added explicit mathematical equations in the revised Method section detailing the computation and ordering process, which relies solely on the data structure and the chosen truncation level without additional dataset-specific parameters. revision: yes
Referee: Results section (quantitative comparisons): The assertions of 'close to Tucker' quality and outperforming CPD require tabulated metrics (e.g., PSNR/SSIM values, exact runtime figures) with clear baseline implementations and, ideally, statistical tests; qualitative statements alone are insufficient to substantiate the load-bearing claims about accuracy-runtime trade-offs.

Authors: We agree that quantitative evidence is crucial. The original manuscript presented results primarily through figures and descriptive text. We have now incorporated a table summarizing PSNR and SSIM values for various truncation levels across the two datasets, along with average runtime measurements for our method, Tucker decomposition, and CPD. Baseline implementations are detailed in the revised text. Due to the small number of test volumes, formal statistical tests were not included, but the numerical results clearly demonstrate the trade-offs. revision: yes

Circularity Check

0 steps flagged

No circularity: method is a direct SVD extension with independent empirical validation

full rationale

The paper introduces Structured 3D-SVD as an extension of matrix SVD logic to third-order volumes, using ordered quasi-singular coefficients for progressive reconstruction. No equations or claims reduce the central performance results (reconstruction quality vs. Tucker/CPD) to fitted parameters, self-definitions, or self-citation chains. Experiments on two fixed biological volumes (fish, brain) are presented as direct evaluation without dataset-specific tuning described as part of the derivation. The derivation chain remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 1 invented entities

Abstract-only view yields no explicit free parameters, axioms, or invented entities beyond the high-level description of the method; truncation levels for progressive reconstruction are implied but not quantified.

free parameters (1)

truncation levels
Levels at which reconstruction is stopped; chosen to balance main structure preservation against detail, but no specific values or fitting procedure given.

axioms (1)

domain assumption Biological volumetric data admit a structured low-rank representation via ordered quasi-singular coefficients that preserves essential spatial features.
Invoked implicitly to justify why the SVD-inspired ordering works for fish and brain scans.

invented entities (1)

quasi-singular coefficients no independent evidence
purpose: Provide an ordered basis for progressive reconstruction of third-order volumes.
Introduced as the key mechanism enabling the structured 3D-SVD approach.

pith-pipeline@v0.9.0 · 5452 in / 1388 out tokens · 48608 ms · 2026-05-10T07:08:36.570761+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

23 extracted references · 23 canonical work pages

[1]

Tensor decompositions and applications

Kolda, T.G.; Bader, B.W. Tensor decompositions and applications. SIAM Rev. 2009, 51, 455

work page 2009
[2]

https://doi.org/10.1137/07070111X

work page doi:10.1137/07070111x
[3]

A multilinear sin gu- lar value decomposition

De Lathauwer, L.; De Moor, B.; Vandewalle, J. A multilinear singular value decomposition. SIAM J. Matrix Anal. Appl. 2000, 21, 1253 1278. https://doi.org/10.1137/S0895479896305696

work page doi:10.1137/s0895479896305696 2000
[4]

Factorization strategies for third-order tensors

Kilmer, M.E.; Martin, C.D. Factorization strategies for third -order tensors. Linear Algebra Appl. 2011, 435, 641 658. https://doi.org/10.1016/j.laa.2010.09.020

work page doi:10.1016/j.laa.2010.09.020 2011
[5]

Towards quantum tensor decomposition in biomedical applications

Burch, M.; Zhang, J.; Idumah, G.; Doga, H.; Lartey, R.; Yehia, L.; Yang, M.; Yildirim, M.; Karaayvaz, M.; Shehab, O.; et al. Towards quantum tensor decomposition in biomedical applications. arXiv 2025, arXiv:2502.13140. https://doi.org/10.48550/arXiv.2502.13140

work page doi:10.48550/arxiv.2502.13140 2025
[6]

Rank- one Approximation to High Order Tensors

Zhang, T.; Golub, G.H. Rank- one Approximation to High Order Tensors. SIAM J. Matrix Anal. Appl. 2001, 23, 534 550. https://doi.org/10.1137/S0895479899352045

work page doi:10.1137/s0895479899352045 2001
[7]

Tensor Eigenvalues and Their Applications; Springer: Singapore, 2018

Qi, L.; Chen, H.; Chen, Y . Tensor Eigenvalues and Their Applications; Springer: Singapore, 2018. https://www.springerprofessional.de/en/tensor-eigenvalues-and-theirapplications/15581194

work page arXiv 2018
[8]

Theory and Computation of Complex Tensors and Its Applications; Springer: Singapore, 2020

Che, M.; Wei, Y . Theory and Computation of Complex Tensors and Its Applications; Springer: Singapore, 2020. https://doi.org/10.1007/978-981-15-2059-4

work page doi:10.1007/978-981-15-2059-4 2020
[9]

Incomplete multi-view clustering via efficient anchor tensor recovery framework

Ji, J.; He, Z.; Jiao, L.; Liu, X.; Pan, J.-S. Incomplete multi-view clustering via efficient anchor tensor recovery framework. Neural Netw. 2025, 190, 107652. https://doi.org/10.1016/j.neunet.2025.107652

work page doi:10.1016/j.neunet.2025.107652 2025
[10]

Low -Rank Approximation of Multi -Way Arrays: A Simple Algorithm for Localized Canonical Polyadic Decomposition

Zhou, G.; Cichocki, A.; Xie, S. Low -Rank Approximation of Multi -Way Arrays: A Simple Algorithm for Localized Canonical Polyadic Decomposition. IEEE Trans. Image Process. 2017, 26, 2119 2131. https://doi.org/10.1109/TIP.2017.2672439

work page doi:10.1109/tip.2017.2672439 2017
[11]

Martin, R

Martin, C.D.; Shafer, R.; LaRue, B. An Order -p Tensor Factorization with Applications in Imaging. SIAM J. Sci. Comput. 2013, 35, A474 A490. https://doi.org/10.1137/110841229

work page doi:10.1137/110841229 2013
[12]

Compression of hyper spectral images using tensor decomposition methods

Sucharitha, B.; Sheela, G.A. Compression of hyper spectral images using tensor decomposition methods. Int. J. Circuits Syst. Signal Process. 2022, 16, 1148 1155. https://doi.org/10.46300/9106.2022.16.138

work page doi:10.46300/9106.2022.16.138 2022
[13]

Overlapping patch-based joint-sparse regression for hyperspectral image unmixing

Shu, S.; He, Z.; Jiao, L.; Liu, X.; Pan, J.- S. Overlapping patch-based joint-sparse regression for hyperspectral image unmixing. J. Comput. Appl. Math. 2026, 472, 116787. https://doi.org/10.1016/j.cam.2025.116787

work page doi:10.1016/j.cam.2025.116787 2026
[14]

Compression of M-FISH images using 3D ESCOT

Xu, J.; Xiong, Z.; Wu, Q.; Li, S. Compression of M-FISH images using 3D ESCOT. In Proceedings of the 2001 International Conference on Image Processing (ICIP 2001); IEEE: Thessaloniki, Greece, 2001; V olume 2, pp. 109 112. https://doi.org/10.1109/ICIP.2001.958436

work page doi:10.1109/icip.2001.958436 2001
[15]

Compression of V olume -Surface Integral Equation Matrices via Tucker Decomposition for Magnetic Resonance Applications

Giannakopoulos, I.I.; Guryev, G.D.; SerrallØs, J.E.C.; Georgakis, I.P.; Daniel, L.; White, J.K.; Lattanzi, R. Compression of V olume -Surface Integral Equation Matrices via Tucker Decomposition for Magnetic Resonance Applications. IEEE Trans. Antennas Propag. 2022, 70, 459 471. https://doi.org/10.1109/TAP.2021.3090835

work page doi:10.1109/tap.2021.3090835 2022
[16]

A tensor-train reduced basis solver for parameterized partial differential equations on Cartesian grids

Mueller, N.; Zhao, Y .; Badia, S.; Cui, T. A tensor-train reduced basis solver for parameterized partial differential equations on Cartesian grids. J. Comput. Appl. Math. 2026, 472, 116790. https://doi.org/10.1016/j.cam.2025.116790. 19

work page doi:10.1016/j.cam.2025.116790 2026
[17]

Low tensor train and low multilinear rank approximations of 3D tensors for compression and despeckling of optical coherence tomography images

Kopriva, I.; Shi, F.; Lai, M.; tanfel, M.; Chen, H.; Chen, X. Low tensor train and low multilinear rank approximations of 3D tensors for compression and despeckling of optical coherence tomography images. Phys. Med. Biol. 2023, 68, 125002. https://doi.org/10.1088/1361-6560/acd6d1

work page doi:10.1088/1361-6560/acd6d1 2023
[18]

Yamagishi, N

Papadacci, C.; Finel, V .; Provost, J.; Villemain, O.; Bruneval, P.; Gennisson, J.L.; Tanter, M.; Fink, M.; Pernot, M. Imaging the dynamics of cardiac fiber orientation in vivo using 3D ultrasound backscatter tensor imaging. Sci. Rep. 2017, 7, 830. https://doi.org/10.1038/s41598- 017-00946-7

work page doi:10.1038/s41598- 2017
[19]

Tensorial Tomographic Differential Phase-Contrast Microscopy

Xu, S.; Dai, X.; Yang, X.; Zhou, K.C.; Kim, K.; Pathak, V .; Glass, C.; Horstmeyer, R. Tensorial Tomographic Differential Phase-Contrast Microscopy. In Proceedings of the 2022 IEEE International Conference on Computational Photography (ICCP); IEEE: Gainesville, FL, USA, 2022; pp. 1 11. https://doi.org/10.1109/ICCP54855.2022.9887674

work page doi:10.1109/iccp54855.2022.9887674 2022
[20]

Diffusible iodine-based contrast-enhanced computed tomography (diceCT): An emerging tool for rapid, high-resolution, 3D imaging of metazoan soft tissues

Gignac, P.M.; Kley, N.J.; Clarke, J.A.; Colbert, M.W.; Morhardt, A.C.; Cerio, D.G.; Cost, I.N.; Cox, C.L.; Daza, J.D.; Early, C.M.; et al. Diffusible iodine-based contrast-enhanced computed tomography (diceCT): An emerging tool for rapid, high-resolution, 3D imaging of metazoan soft tissues. J. Anat. 2016, 228, 889 909. https://doi.org/10.1111/joa.12449

work page doi:10.1111/joa.12449 2016
[21]

MorphoSource: Archiving and sharing 3-D digital specimen data

McGeary, T.; Boyer, D.M.; Gunnell, G.F.; Kaufman, S. MorphoSource: Archiving and sharing 3-D digital specimen data. Paleontol. Soc. Pap. 2016, 22, 157 181. https://doi.org/10.1017/scs.2017.13

work page doi:10.1017/scs.2017.13 2016
[22]

Tensor Methods in Biomedical Image Analysis

Sedighin, F.; Roehe, R.; Moghaddam, M.E.; Richards, J.P. Tensor Methods in Biomedical Image Analysis. J. Med. Signals Sens. 2024, 14, 16. https://doi.org/10.4103/jmss.jmss_55_23

work page doi:10.4103/jmss.jmss_55_23 2024
[23]

Fluorescence microscopy tensor imaging representations for large -scale dataset analysis

Vinegoni, C.; Feruglio, P.F.; Weissleder, R. Fluorescence microscopy tensor imaging representations for large -scale dataset analysis. Sci. Rep. 2020, 10, 6328. https://doi.org/10.1038/s41598-020-62233-2. [23] Chen, J.; Wei, Y .; Zhang, G. Tensor generalized Schur decomposition and its applications. J. Sci. Comput. 2026, 106, 31. https://doi.org/10.1007/s...

work page doi:10.1038/s41598-020-62233-2 2020

[1] [1]

Tensor decompositions and applications

Kolda, T.G.; Bader, B.W. Tensor decompositions and applications. SIAM Rev. 2009, 51, 455

work page 2009

[2] [2]

https://doi.org/10.1137/07070111X

work page doi:10.1137/07070111x

[3] [3]

A multilinear sin gu- lar value decomposition

De Lathauwer, L.; De Moor, B.; Vandewalle, J. A multilinear singular value decomposition. SIAM J. Matrix Anal. Appl. 2000, 21, 1253 1278. https://doi.org/10.1137/S0895479896305696

work page doi:10.1137/s0895479896305696 2000

[4] [4]

Factorization strategies for third-order tensors

Kilmer, M.E.; Martin, C.D. Factorization strategies for third -order tensors. Linear Algebra Appl. 2011, 435, 641 658. https://doi.org/10.1016/j.laa.2010.09.020

work page doi:10.1016/j.laa.2010.09.020 2011

[5] [5]

Towards quantum tensor decomposition in biomedical applications

Burch, M.; Zhang, J.; Idumah, G.; Doga, H.; Lartey, R.; Yehia, L.; Yang, M.; Yildirim, M.; Karaayvaz, M.; Shehab, O.; et al. Towards quantum tensor decomposition in biomedical applications. arXiv 2025, arXiv:2502.13140. https://doi.org/10.48550/arXiv.2502.13140

work page doi:10.48550/arxiv.2502.13140 2025

[6] [6]

Rank- one Approximation to High Order Tensors

Zhang, T.; Golub, G.H. Rank- one Approximation to High Order Tensors. SIAM J. Matrix Anal. Appl. 2001, 23, 534 550. https://doi.org/10.1137/S0895479899352045

work page doi:10.1137/s0895479899352045 2001

[7] [7]

Tensor Eigenvalues and Their Applications; Springer: Singapore, 2018

Qi, L.; Chen, H.; Chen, Y . Tensor Eigenvalues and Their Applications; Springer: Singapore, 2018. https://www.springerprofessional.de/en/tensor-eigenvalues-and-theirapplications/15581194

work page arXiv 2018

[8] [8]

Theory and Computation of Complex Tensors and Its Applications; Springer: Singapore, 2020

Che, M.; Wei, Y . Theory and Computation of Complex Tensors and Its Applications; Springer: Singapore, 2020. https://doi.org/10.1007/978-981-15-2059-4

work page doi:10.1007/978-981-15-2059-4 2020

[9] [9]

Incomplete multi-view clustering via efficient anchor tensor recovery framework

Ji, J.; He, Z.; Jiao, L.; Liu, X.; Pan, J.-S. Incomplete multi-view clustering via efficient anchor tensor recovery framework. Neural Netw. 2025, 190, 107652. https://doi.org/10.1016/j.neunet.2025.107652

work page doi:10.1016/j.neunet.2025.107652 2025

[10] [10]

Low -Rank Approximation of Multi -Way Arrays: A Simple Algorithm for Localized Canonical Polyadic Decomposition

Zhou, G.; Cichocki, A.; Xie, S. Low -Rank Approximation of Multi -Way Arrays: A Simple Algorithm for Localized Canonical Polyadic Decomposition. IEEE Trans. Image Process. 2017, 26, 2119 2131. https://doi.org/10.1109/TIP.2017.2672439

work page doi:10.1109/tip.2017.2672439 2017

[11] [11]

Martin, R

Martin, C.D.; Shafer, R.; LaRue, B. An Order -p Tensor Factorization with Applications in Imaging. SIAM J. Sci. Comput. 2013, 35, A474 A490. https://doi.org/10.1137/110841229

work page doi:10.1137/110841229 2013

[12] [12]

Compression of hyper spectral images using tensor decomposition methods

Sucharitha, B.; Sheela, G.A. Compression of hyper spectral images using tensor decomposition methods. Int. J. Circuits Syst. Signal Process. 2022, 16, 1148 1155. https://doi.org/10.46300/9106.2022.16.138

work page doi:10.46300/9106.2022.16.138 2022

[13] [13]

Overlapping patch-based joint-sparse regression for hyperspectral image unmixing

Shu, S.; He, Z.; Jiao, L.; Liu, X.; Pan, J.- S. Overlapping patch-based joint-sparse regression for hyperspectral image unmixing. J. Comput. Appl. Math. 2026, 472, 116787. https://doi.org/10.1016/j.cam.2025.116787

work page doi:10.1016/j.cam.2025.116787 2026

[14] [14]

Compression of M-FISH images using 3D ESCOT

Xu, J.; Xiong, Z.; Wu, Q.; Li, S. Compression of M-FISH images using 3D ESCOT. In Proceedings of the 2001 International Conference on Image Processing (ICIP 2001); IEEE: Thessaloniki, Greece, 2001; V olume 2, pp. 109 112. https://doi.org/10.1109/ICIP.2001.958436

work page doi:10.1109/icip.2001.958436 2001

[15] [15]

Compression of V olume -Surface Integral Equation Matrices via Tucker Decomposition for Magnetic Resonance Applications

Giannakopoulos, I.I.; Guryev, G.D.; SerrallØs, J.E.C.; Georgakis, I.P.; Daniel, L.; White, J.K.; Lattanzi, R. Compression of V olume -Surface Integral Equation Matrices via Tucker Decomposition for Magnetic Resonance Applications. IEEE Trans. Antennas Propag. 2022, 70, 459 471. https://doi.org/10.1109/TAP.2021.3090835

work page doi:10.1109/tap.2021.3090835 2022

[16] [16]

A tensor-train reduced basis solver for parameterized partial differential equations on Cartesian grids

Mueller, N.; Zhao, Y .; Badia, S.; Cui, T. A tensor-train reduced basis solver for parameterized partial differential equations on Cartesian grids. J. Comput. Appl. Math. 2026, 472, 116790. https://doi.org/10.1016/j.cam.2025.116790. 19

work page doi:10.1016/j.cam.2025.116790 2026

[17] [17]

Low tensor train and low multilinear rank approximations of 3D tensors for compression and despeckling of optical coherence tomography images

Kopriva, I.; Shi, F.; Lai, M.; tanfel, M.; Chen, H.; Chen, X. Low tensor train and low multilinear rank approximations of 3D tensors for compression and despeckling of optical coherence tomography images. Phys. Med. Biol. 2023, 68, 125002. https://doi.org/10.1088/1361-6560/acd6d1

work page doi:10.1088/1361-6560/acd6d1 2023

[18] [18]

Yamagishi, N

Papadacci, C.; Finel, V .; Provost, J.; Villemain, O.; Bruneval, P.; Gennisson, J.L.; Tanter, M.; Fink, M.; Pernot, M. Imaging the dynamics of cardiac fiber orientation in vivo using 3D ultrasound backscatter tensor imaging. Sci. Rep. 2017, 7, 830. https://doi.org/10.1038/s41598- 017-00946-7

work page doi:10.1038/s41598- 2017

[19] [19]

Tensorial Tomographic Differential Phase-Contrast Microscopy

Xu, S.; Dai, X.; Yang, X.; Zhou, K.C.; Kim, K.; Pathak, V .; Glass, C.; Horstmeyer, R. Tensorial Tomographic Differential Phase-Contrast Microscopy. In Proceedings of the 2022 IEEE International Conference on Computational Photography (ICCP); IEEE: Gainesville, FL, USA, 2022; pp. 1 11. https://doi.org/10.1109/ICCP54855.2022.9887674

work page doi:10.1109/iccp54855.2022.9887674 2022

[20] [20]

Diffusible iodine-based contrast-enhanced computed tomography (diceCT): An emerging tool for rapid, high-resolution, 3D imaging of metazoan soft tissues

Gignac, P.M.; Kley, N.J.; Clarke, J.A.; Colbert, M.W.; Morhardt, A.C.; Cerio, D.G.; Cost, I.N.; Cox, C.L.; Daza, J.D.; Early, C.M.; et al. Diffusible iodine-based contrast-enhanced computed tomography (diceCT): An emerging tool for rapid, high-resolution, 3D imaging of metazoan soft tissues. J. Anat. 2016, 228, 889 909. https://doi.org/10.1111/joa.12449

work page doi:10.1111/joa.12449 2016

[21] [21]

MorphoSource: Archiving and sharing 3-D digital specimen data

McGeary, T.; Boyer, D.M.; Gunnell, G.F.; Kaufman, S. MorphoSource: Archiving and sharing 3-D digital specimen data. Paleontol. Soc. Pap. 2016, 22, 157 181. https://doi.org/10.1017/scs.2017.13

work page doi:10.1017/scs.2017.13 2016

[22] [22]

Tensor Methods in Biomedical Image Analysis

Sedighin, F.; Roehe, R.; Moghaddam, M.E.; Richards, J.P. Tensor Methods in Biomedical Image Analysis. J. Med. Signals Sens. 2024, 14, 16. https://doi.org/10.4103/jmss.jmss_55_23

work page doi:10.4103/jmss.jmss_55_23 2024

[23] [23]

Fluorescence microscopy tensor imaging representations for large -scale dataset analysis

Vinegoni, C.; Feruglio, P.F.; Weissleder, R. Fluorescence microscopy tensor imaging representations for large -scale dataset analysis. Sci. Rep. 2020, 10, 6328. https://doi.org/10.1038/s41598-020-62233-2. [23] Chen, J.; Wei, Y .; Zhang, G. Tensor generalized Schur decomposition and its applications. J. Sci. Comput. 2026, 106, 31. https://doi.org/10.1007/s...

work page doi:10.1038/s41598-020-62233-2 2020