mlsanityData to 14 Oct 2026

Quasi-SVD: Learning a Lie-constrained matrix factorisation for real-time imaging

arXiv 2607.25967 ↗First posted 28 Jul 2026cs.CV cs.LG cs.NAcited by 0

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Abstract (arXiv)

Singular Value Decomposition (SVD) underlies matrix factorisation tasks across many fields, with imaging applications demanding real-time processing. Yet SVD algorithms are inherently sequential, constraining real-time GPU throughput and limit online deployment in imaging pipelines. This study introduces a fully parallelized matrix factorization framework for GPUs by enforcing matrix orthogonality on left singular vectors via Lie-parametrised algebra and recovering the remaining components through soft constraints. This asymmetric constraint design enables an efficient parallel and provably valid decomposition, achieves high reconstruction fidelity and substantially accelerates computation relative to the exact SVD, with real-time throughput exceeding standard video frame rates. Performance is evaluated on multiple imaging tasks spanning complementary computational regimes: (1) spatio-temporal background subtraction for ultrasound localisation microscopy, requiring high-dimensional matrix separation, (2) Mueller matrix polarimetry for neurosurgical tissue characterisation, requiring massive batch processing of small matrices, and (3) an MNIST denoising benchmark at an intermediate scale with known ground truth. Across regimes and instruments, the proposed framework demonstrates robust domain transfer at various matrix scales, sufficient for live image-guided workflows that classical solvers cannot currently support in these settings. By prioritising downstream reconstruction fidelity over exact spectral recovery, the proposed SVD framework makes structured matrix factorisation practical for real-time processing.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 21 of its 52 references that are in the map. First posted on arXiv 28 Jul 2026.

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21 of 52 references.

References · 21

  1. 2018fastMRI: An Open Dataset and Benchmarks for Accelerated MRIcited by 470
  2. 2023Gaussian Splatting SLAMcited by 415
  3. 2024SVD-LLM: Truncation-aware Singular Value Decomposition for Large Language Model Compressioncited by 243
  4. 2019Cheap Orthogonal Constraints in Neural Networks: A Simple Parametrization of the Orthogonal and Unitary Groupcited by 134
  5. 2020Efficient Riemannian Optimization on the Stiefel Manifold via the Cayley Transformcited by 80
  6. 2019Deep Spectral Clustering using Dual Autoencoder Networkcited by 71
  7. 2015Randomized Block Krylov Methods for Stronger and Faster Approximate Singular Value Decompositioncited by 64
  8. 2017Tensor SVD: Statistical and Computational Limitscited by 53
  9. 2023Learning How To Robustly Estimate Camera Pose in Endoscopic Videoscited by 50
  10. 2021Tangent Space Backpropagation for 3D Transformation Groupscited by 40
  11. 2019Deep K-SVD Denoisingcited by 26
  12. 2025QSVD: Efficient Low-rank Approximation for Unified Query-Key-Value Weight Compression in Low-Precision Vision-Language Modelscited by 16
9 more
  1. 2024Operator SVD with Neural Networks via Nested Low-Rank Approximationcited by 13
  2. 2025DiTASK: Multi-Task Fine-Tuning with Diffeomorphic Transformationscited by 7
  3. 2019Learned SVD: solving inverse problems via hybrid autoencodingcited by 5
  4. 2021Efficient GPU implementation of randomized SVD and its applicationscited by 5
  5. 2015Background Subtraction via Generalized Fused Lasso Foreground Modelingcited by 4
  6. 2024Physically Consistent Image Augmentation for Deep Learning in Mueller Matrix Polarimetrycited by 2
  7. 2014A hierarchically blocked Jacobi SVD algorithm for single and multiple graphics processing unitscited by 1
  8. 2023RF-ULM: Ultrasound Localization Microscopy Learned from Radio-Frequency Wavefrontscited by 1
  9. 2024Near-Real-Time Mueller Polarimetric Image Processing for Neurosurgical Interventioncited by 1

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