L-SR1: Learned Symmetric-Rank-One Preconditioning

End-to-end deep learning has achieved impressive results but remains limited by its reliance on large labeled datasets, poor generalization to unseen scenarios, and growing computational demands. In contrast, classical optimization methods are data-efficient and lightweight but often suffer from slow convergence. While learned optimizers offer a promising fusion of both worlds, most focus on first-order methods, leaving learned second-order approaches largely unexplored. We propose a novel learned second-order optimizer that introduces a trainable preconditioning unit to enhance the classical Symmetric-Rank-One (SR1) algorithm. This unit generates data-driven vectors used to construct positive semi-definite rank-one matrices, aligned with the secant constraint via a learned projection. Our method is evaluated through analytic experiments and on the real-world task of Monocular Human Mesh Recovery (HMR), where it outperforms existing learned optimization-based approaches. Featuring a lightweight model and requiring no annotated data or fine-tuning, our approach offers strong generalization and is well-suited for integration into broader optimization-based frameworks.

CardioSpectrum: Comprehensive Myocardium Motion Analysis with 3D Deep Learning and Geometric Insights

The ability to map left ventricle (LV) myocardial motion using computed tomography angiography (CTA) is essential to diagnosing cardiovascular conditions and guiding interventional procedures. Due to their inherent locality, conventional neural networks typically have difficulty predicting subtle tangential movements, which considerably lessens the level of precision at which myocardium three-dimensional (3D) mapping can be performed. Using 3D optical flow techniques and Functional Maps (FMs), we present a comprehensive approach to address this problem. FMs are known for their capacity to capture global geometric features, thus providing a fuller understanding of 3D geometry. As an alternative to traditional segmentation-based priors, we employ surface-based two-dimensional (2D) constraints derived from spectral correspondence methods. Our 3D deep learning architecture, based on the ARFlow model, is optimized to handle complex 3D motion analysis tasks. By incorporating FMs, we can capture the subtle tangential movements of the myocardium surface precisely, hence significantly improving the accuracy of 3D mapping of the myocardium. The experimental results confirm the effectiveness of this method in enhancing myocardium motion analysis. This approach can contribute to improving cardiovascular diagnosis and treatment. Our code and additional resources are available at: https://shaharzuler.github.io/CardioSpectrumPage

Synthetic Data Generation for 3D Myocardium Deformation Analysis

Accurate analysis of 3D myocardium deformation using high-resolution computerized tomography (CT) datasets with ground truth (GT) annotations is crucial for advancing cardiovascular imaging research. However, the scarcity of such datasets poses a significant challenge for developing robust myocardium deformation analysis models. To address this, we propose a novel approach to synthetic data generation for enriching cardiovascular imaging datasets. We introduce a synthetic data generation method, enriched with crucial GT 3D optical flow annotations. We outline the data preparation from a cardiac four-dimensional (4D) CT scan, selection of parameters, and the subsequent creation of synthetic data from the same or other sources of 3D cardiac CT data for training. Our work contributes to overcoming the limitations imposed by the scarcity of high-resolution CT datasets with precise annotations, thereby facilitating the development of accurate and reliable myocardium deformation analysis algorithms for clinical applications and diagnostics. Our code is available at: http://www.github.com/shaharzuler/cardio_volume_skewer