Abstract EigenDecomposition (ED) is at the heart of many computer vision algorithms and applications. One crucial bottleneck limiting its usage is the expensive computation cost, particularly for a mini-batch of matrices in deep neural networks. Our previous work proposed a dedicated QR-based ED algorithm for batched small matrices (dim< 32 {<}32 < 32 64 64 64
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Jul 28, 2026 · cs.CV J/K move · Enter open · S save
Christopher Hahne
University of Bern 3008 Bern, Switzerland
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.