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.

翻译：逆问题本质上是病态的，存在非唯一性和不稳定性。经典的正则化方法提供了数学上严谨的解决方案，确保了稳定性和收敛性，但通常以牺牲灵活性或视觉质量为代价。基于学习的重建方法，例如卷积神经网络，可以产生视觉上引人注目的结果，但它们通常缺乏严格的理论保证。DC网络通过在网络架构中强制执行测量模型来解决这一差距。具体而言，将零空间网络与作为初始重建的经典正则化方法相结合，定义了一种收敛的正则化方法。这种方法在保持经典方案理论可靠性的同时，利用了数据驱动学习的表达能力，从而产生既准确又视觉上吸引人的重建结果。