Computational imaging has been revolutionized by compressed sensing algorithms, which offer guaranteed uniqueness, convergence, and stability properties. Model-based deep learning methods that combine imaging physics with learned regularization priors have emerged as more powerful alternatives for image recovery. The main focus of this paper is to introduce a memory efficient model-based algorithm with similar theoretical guarantees as CS methods. The proposed iterative algorithm alternates between a gradient descent involving the score function and a conjugate gradient algorithm to encourage data consistency. The score function is modeled as a monotone convolutional neural network. Our analysis shows that the monotone constraint is necessary and sufficient to enforce the uniqueness of the fixed point in arbitrary inverse problems. In addition, it also guarantees the convergence to a fixed point, which is robust to input perturbations. We introduce two implementations of the proposed MOL framework, which differ in the way the monotone property is imposed. The first approach enforces a strict monotone constraint, while the second one relies on an approximation. The guarantees are not valid for the second approach in the strict sense. However, our empirical studies show that the convergence and robustness of both approaches are comparable, while the less constrained approximate implementation offers better performance. The proposed deep equilibrium formulation is significantly more memory efficient than unrolled methods, which allows us to apply it to 3D or 2D+time problems that current unrolled algorithms cannot handle.
翻译:压缩感测算法使计算成像发生了革命性的变化,这种算法提供了有保障的独特性、趋同性和稳定性特性。基于模型的深层次学习方法将成像物理学与学习的正规化前科相结合,这些方法已成为恢复图像的更强有力的替代方法。本文件的主要重点是引入一个记忆高效模型算法,其理论保障与CS方法相似。提议的迭代算法在涉及得分函数的梯度下降和鼓励数据一致性的同梯度算法之间互换。评分函数以单调共振神经网络为模型。我们的分析表明,单调限制对于在任意反问题中执行固定点的独特性是必要和充分的。此外,它还保证了与固定点的趋同性,而这种固定点对投入的扰动是有力的。我们引入了两个拟议的MOL框架,其实施单一属性的方式不同。第一个方法是严格的单调制限制,而第二个方法则依赖于近似性。从严格意义上看,保证对第二种方法是无效的。然而,我们的实验性研究显示,趋同性和稳性方法不能使我们更接近于当前3级的形成更接近性。</s>