We introduce a monotone deep equilibrium learning framework for large-scale inverse problems in imaging. The proposed algorithm relies on forward-backward splitting, where each iteration consists of 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. The use of a monotone operator offers several benefits, including guaranteed convergence, uniqueness of fixed point, and robustness to input perturbations, similar to the use of convex priors in compressive sensing. In addition, the proposed formulation is significantly more memory-efficient than unrolled methods, which allows us to apply it to 3D problems that current unrolled algorithms cannot handle. Experiments show that the proposed scheme can offer improved performance in 3D settings while being stable in the presence of input perturbations.

介绍一种记忆效率高、具有计算成像和深度学习特性的算法，该算法利用了先前压缩感知算法提供的独特性、收敛性和稳定性特点，使用循环梯度下降和共轭梯度算法交替应用以实现数据一致性，同时模拟了单调卷积神经网络的得分函数，保证了输出唯一性和收敛性，而且提出的深度平衡公式比现有算法更省内存，能够处理现有算法无法处理的三维或2D +时间问题。

具有收敛性和稳健性保证的存储效率模型的深度学习