发表机构
Physikalisch-Technische Bundesanstalt (PTB); University of Cambridge; University of Genoa; Queen Mary University of London（德国联邦物理技术研究院; 剑桥大学; 热那亚大学; 伦敦大学玛丽女王学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出DREAM方法，通过算法展开在零样本自监督场景下学习TV和TGV的自适应正则化图，在图像去噪和动态MRI重建任务中性能优异，零样本训练可媲美监督模型，且计算效率更高、可解释性强。
AI 中文摘要
自适应正则化是提升经典变分重建方法灵活性的有效手段，同时保留其可解释性和数学结构。本研究在零样本自监督场景下，提出一种通过算法展开学习深度重参数化自适应正则化图（DREAM）的方法，用于总变分（TV）和总广义变分（TGV），无需访问大型配对数据集。我们首先在二维图像去噪问题上验证DREAM，随后将其应用于大规模动态MRI重建。所得自适应模型具有理论依据，保留了作为展开架构构建块的原始对偶算法的收敛特性。结果表明，正则化参数图可被高效学习，与现有最优方法相比，达到相当性能所需的权重更新次数显著更少。我们进一步证明，图的CNN参数化作为隐式先验提供了有效的降维，优于自适应参数的直接优化。在两个应用中，DREAM的监督训练与零样本训练之间的性能差距小于所对比的端到端深度学习方法。值得注意的是，在动态心脏MRI重建中，零样本训练的性能与监督模型相当。此外，所学自适应图具有高度可解释性，在难以获取参考数据时，为纯深度学习方法提供了极具吸引力的替代方案。
英文摘要
Adaptive regularization is an effective means of improving the flexibility of classical variational reconstruction methods while retaining their interpretability and mathematical structure. In this work, we propose an approach for learning deep-reparameterized adaptive regularization maps (DREAM) for Total Variation (TV) and Total Generalized Variation (TGV) through algorithm unrolling in a zero-shot, self-supervised setting, requiring no access to large paired datasets. We first validate DREAM on a two-dimensional image-denoising problem and then apply it to large-scale dynamic MRI reconstruction. The resulting adaptive models are theoretically grounded, as they retain the convergence properties of the primal-dual algorithm used as the building block of the unrolled architecture. Our results show that the regularization parameter maps can be learned efficiently, requiring substantially fewer weight updates than state-of-the-art methods to achieve comparable performance. We further demonstrate that the CNN parametrization of the maps acts as an implicit prior and provides effective dimensionality reduction, outperforming direct optimization of the adaptive parameters. Across both applications, the performance gap between supervised and zero-shot training is smaller for DREAM than for the end-to-end deep-learning methods considered for comparison. Remarkably, in dynamic cardiac MRI reconstruction, zero-shot training matches the performance of the supervised model. Moreover, the learned adaptive maps are highly interpretable, providing a compelling alternative to purely deep-learning-based methods when reference data are difficult to obtain.
Comments13 pages, 8 figures
