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

Singular Value Decomposition (SVD) underlies matrix factorisation tasks across computational imaging, with medical applications increasingly demanding real-time processing. Yet SVD algorithms are inherently sequential, constraining real-time GPU throughput and limit online deployment in clinical pipelines. This study introduces Quasi-SVD, a differentiable, fully parallelized matrix factorization framework for GPUs. Rather than enforcing orthogonality on both factors, it guarantees exact orthogonality for a single Lie-parameterized factor while recovering the remaining components through soft constraints, enabling efficient parallel decomposition without iterative singular-vector optimization. This asymmetric design, provably sufficient for valid factorisation, achieves reconstruction fidelity of SSIM = 0.89-0.94 and accelerates computation by 3-20x relative to cuSOLVER and randomised SVD, enabling throughput above 25 FPS. Performance is evaluated on two medical imaging tasks spanning complementary computational regimes: (1) spatio-temporal background subtraction for ultrasound localisation microscopy, requiring high-dimensional matrix separation, and (2) Mueller matrix polarimetry for neurosurgical tissue characterisation, requiring massive batch processing of small matrices. Across both regimes and multiple imaging instruments, the proposed framework demonstrates robust domain transfer and throughput exceeding 25 FPS at clinical matrix scales, a rate sufficient for live image-guided workflows that classical solvers cannot currently support in these settings. By prioritising downstream reconstruction fidelity over exact spectral recovery, Quasi-SVD makes structured matrix factorisation practical for real-time imaging.

Panda: Unsupervised Pelvic Anomaly Detection for Real-Time MR Imaging

Female pelvic diseases remain an under researched area characterized by often delayed diagnosis. While pelvic MRI offers superior soft-tissue contrast for diagnosis and image-guided procedures, real-time anomaly detection remains challenging due to physiological motion, tissue deformation, and instrument artifacts. Existing supervised approaches are impractical, as adverse events are rare, heterogeneous, and difficult to annotate. We present a Dinomaly-based unsupervised anomaly detection framework adapted for pelvic MRI that learns normative representations from healthy cases and flags deviations without requiring labels. Our approach leverages a frozen DINOv3 Vision Transformer encoder combined with a noisy MLP bottleneck and Linear Attention decoder to prevent identity mapping while maintaining computational efficiency. Anomalies are localized via per-token cosine distance between encoder and decoder representations, yielding spatial anomaly maps that provide immediate feedback at the scanner to support radiologist decision-making and adaptive protocol adjustment. Evaluated on a curated subset of the Uterine Myoma Dataset, the framework achieves a pixel-level AUROC of 88.06% and high specificity (95.45%) at frame level at 40.5 slices/s, meeting real-time clinical deployment requirements. The spatial anomaly maps and frame-level scores provide immediate, localized feedback at the scanner to support radiologist decision-making and adaptive protocol adjustment during active procedures.