融合数学约束与数据学习，提升逆问题重建的准确性与视觉效果。
Data-Consistent Learning of Inverse Problems
- 在网络中嵌入测量模型，确保重建结果符合物理规律。
- 结合经典正则化与神经网络，实现理论可靠且视觉高质量的重建。
- 适合需要高精度与可解释性的医学成像、信号处理领域使用。
逆问题本质上是病态的，存在解不唯一和不稳定的缺陷。传统正则化方法虽有坚实的数学基础，保障稳定性和收敛性，但常牺牲灵活性或视觉质量。基于数据的学习重建方法（如卷积神经网络）能生成视觉上引人注目的结果，却通常缺乏严格的理论保证。数据一致性（DC）网络通过在架构中强制实施测量模型，弥合了这一差距。具体而言，将零空间网络与经典正则化方法结合作为初始重建，定义了一种收敛的正则化方法。该方法既保持了传统方案的理论可靠性，又利用了数据驱动学习的表达能力，实现了既准确又视觉吸引人的重建效果。
原文摘要 · Abstract (English)
Inverse problems are inherently ill-posed, suffering from non-uniqueness and instability. Classical regularization methods provide mathematically well-founded solutions, ensuring stability and convergence, but often at the cost of reduced flexibility or visual quality. Learned reconstruction methods, such as convolutional neural networks, can produce visually compelling results, yet they typically lack rigorous theoretical guarantees. DC (DC) networks address this gap by enforcing the measurement model within the network architecture. In particular, null-space networks combined with a classical regularization method as an initial reconstruction define a convergent regularization method. This approach preserves the theoretical reliability of classical schemes while leveraging the expressive power of data-driven learning, yielding reconstructions that are both accurate and visually appealing.
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