Numerous tasks at the core of statistics, learning and vision areas are specific cases of ill-posed inverse problems. Recently, learning-based (e.g., deep) iterative methods have been empirically shown to be useful for these problems. Nevertheless, integrating learnable structures into iterations is still a laborious process, which can only be guided by intuitions or empirical insights. Moreover, there is a lack of rigorous analysis about the convergence behaviors of these reimplemented iterations, and thus the significance of such methods is a little bit vague. This paper moves beyond these limits and proposes Flexible Iterative Modularization Algorithm (FIMA), a generic and provable paradigm for nonconvex inverse problems. Our theoretical analysis reveals that FIMA allows us to generate globally convergent trajectories for learning-based iterative methods. Meanwhile, the devised scheduling policies on flexible modules should also be beneficial for classical numerical methods in the nonconvex scenario. Extensive experiments on real applications verify the superiority of FIMA.

提出了一种名为FIMA的灵活迭代模块化算法，可以解决非凸反问题，实现全局收敛，并可以拓展经典数值方法。经过实验证明FIMA在真实应用方面具有优越性。

基于学习的迭代方法在非凸逆问题上的收敛性