Undersampling is a common method in Magnetic Resonance Imaging (MRI) to subsample the number of data points in k-space, reducing acquisition times at the cost of decreased image quality. A popular approach is to employ undersampling patterns following various strategies, e.g., variable density sampling or radial trajectories. In this work, we propose a method that directly learns the undersampling masks from data points, thereby also providing task- and domain-specific patterns. To solve the resulting discrete optimization problem, we propose a general optimization routine called ProM: A fully probabilistic, differentiable, versatile, and model-free framework for mask optimization that enforces acceleration factors through a convex constraint. Analyzing knee, brain, and cardiac MRI datasets with our method, we discover that different anatomic regions reveal distinct optimal undersampling masks, demonstrating the benefits of using custom masks, tailored for a downstream task. For example, ProM can create undersampling masks that maximize performance in downstream tasks like segmentation with networks trained on fully-sampled MRIs. Even with extreme acceleration factors, ProM yields reasonable performance while being more versatile than existing methods, paving the way for data-driven all-purpose mask generation.

翻译：欠采样是磁共振成像（MRI）中一种常用方法，通过子采样k空间数据点数来减少采集时间，但会牺牲图像质量。现有方法通常采用遵循不同策略的欠采样模式，如变密度采样或径向轨迹。本文提出一种直接从数据点学习欠采样掩码的方法，从而获得任务特异性和领域特异性模式。为求解由此产生的离散优化问题，我们提出一种通用优化程序ProM：一种全概率、可微分、通用且无模型的掩码优化框架，通过凸约束施加加速因子。采用本方法分析膝关节、脑部和心脏MRI数据集，我们发现不同解剖区域会呈现不同的最优欠采样掩码，这证明了针对下游任务定制掩码的优势。例如，ProM能生成欠采样掩码，使采用全采样MRI训练网络的下游任务（如分割）性能最大化。即使在极端加速因子下，ProM仍能保持合理性能，同时比现有方法更具通用性，为数据驱动的通用掩码生成铺平道路。