发表机构
University of Bern（伯尔尼大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究针对医学成像实时处理需求，引入可微、完全并行化的Quasi-SVD框架，通过不对称设计保证单因子正交性并软约束恢复其余分量，在医学成像任务中实现高效并行分解，性能优于传统方法，使结构化矩阵分解适用于实时成像。
AI 中文摘要
奇异值分解（SVD）是计算成像中矩阵分解任务的基础，随着医学应用对实时处理需求的增加，而SVD算法本质上是顺序的，限制了实时GPU吞吐量和临床管道中的在线部署。本研究引入了准奇异值分解（Quasi-SVD），这是一种用于GPU的可微、完全并行化的矩阵分解框架。它通过对单个李参数化因子保证精确正交性，同时通过软约束恢复其余分量，实现高效并行分解。在两个医学成像任务上评估性能，结果表明该框架在临床矩阵规模上具有强大的域转移能力和超过25 FPS的吞吐量，证明了其在实时成像中的实用性。
英文摘要
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.
