Dynamic MRI Reconstruction Via Dual Deep Priors and Low-Rank Plus Sparse Modeling
通过双深度先验和低秩加稀疏建模实现动态MRI重建
Yongliang Sun, Siddhant Gautam, Chaoyan Huang, Nicole Seiberlich, Ismail Alkhouri, Saiprasad Ravishankar
AI总结 本文提出了一种结构化的深度图像先验框架,用于动态MRI重建,通过低秩加稀疏分解显式建模时空相关性,结合深度图像先验的隐式正则化和经典低秩加稀疏正则化的可解释性,实现了在动态MRI重建中的优越性能。
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从欠采样测量中重建动态MRI是一个具有挑战性的逆问题,需要在 cine 系列的各个帧之间保持空间重建质量和时间一致性。尽管最近的基于学习的方法表现出强大的性能,但它们严重依赖于大规模训练数据,主要是完全采样的数据集,并且在没有这些数据的情况下可能泛化能力差。相比之下,无需训练数据的方法,如深度图像先验(DIP),可以直接适应个体扫描,但往往无法充分利用时间结构,并且容易过拟合。它们在动态MRI中特别有吸引力,因为存在有限的大型、高质量公开数据集。在本文中,我们提出了一种结构化的DIP框架,用于动态MRI重建,通过低秩加稀疏(L+S)分解显式建模时空相关性。而不是直接重建 cine 图像序列,我们使用两个未训练的卷积神经网络参数化低秩背景和稀疏动态组件,通过加速扩展的ADMM(eADMM)联合优化。这种形式结合了DIP的隐式正则化和经典L+S正则化的可解释性。我们为所提出的eADMM算法在基于DIP的非凸参数化情况下的收敛性分析提供了证明。特别是,我们建立了充分下降性质,并证明了生成序列的每一个聚类点都是相关Lyapunov函数的临界点。在各种加速因子下,我们的数值结果表明,所提出的方法在各种加速因子下,始终优于经典重建和现有的监督和非监督MRI重建技术。
Dynamic MRI reconstruction from undersampled measurements is a challenging inverse problem that requires preserving both spatial reconstruction quality and temporal consistency across the frames of the cine series. While recent learning-based approaches achieve strong performance, they heavily rely on large training, mostly fully sampled, datasets, and may otherwise generalize poorly. In contrast, training-data-free methods such as deep image prior (DIP) adapt directly to individual scans but often fail to fully exploit temporal structure and are prone to overfitting. They are particularly attractive for dynamic MRI due to the limited large, public, high-quality datasets. In this work, we propose a structured DIP framework for dynamic MRI reconstruction that explicitly models spatiotemporal correlations through a low-rank plus sparse (L+S) decomposition. Instead of directly reconstructing the cine image series, we parameterize the low-rank background and sparse dynamic components using two DIP untrained convolutional neural networks, jointly optimized using accelerated extrapolated ADMM (eADMM). This formulation combines the implicit regularization of DIP with the interpretability of classical L+S regularization. We provide a convergence analysis for the proposed eADMM algorithm in the presence of DIP-based nonconvex parameterizations. In particular, we establish a sufficient descent property and show that every cluster point of the generated sequence is a critical point of the associated Lyapunov function. Across various acceleration factors, our numerical results demonstrate that the proposed method consistently outperforms classical reconstruction and existing supervised and unsupervised MRI reconstruction techniques.