Convex Latent-Optimized Adversarial Regularizers for Imaging Inverse
  Problems
Huayu Wang Chen Luo Taofeng Xie Qiyu Jin Guoqing Chen Zhuo-Xu Cui Dong Liang
Recently, data-driven techniques have demonstrated remarkable effectiveness
in addressing challenges related to MR imaging inverse problems. However, these
methods still exhibit certain limitations in terms of interpretability and
robustness. In response, we introduce Convex Latent-Optimized Adversarial
Regularizers (CLEAR), a novel and interpretable data-driven paradigm. CLEAR
represents a fusion of deep learning (DL) and variational regularization.
Specifically, we employ a latent optimization technique to adversarially train
an input convex neural network, and its set of minima can fully represent the
real data manifold. We utilize it as a convex regularizer to formulate a
CLEAR-informed variational regularization model that guides the solution of the
imaging inverse problem on the real data manifold. Leveraging its inherent
convexity, we have established the convergence of the projected subgradient
descent algorithm for the CLEAR-informed regularization model. This convergence
guarantees the attainment of a unique solution to the imaging inverse problem,
subject to certain assumptions. Furthermore, we have demonstrated the
robustness of our CLEAR-informed model, explicitly showcasing its capacity to
achieve stable reconstruction even in the presence of measurement interference.
Finally, we illustrate the superiority of our approach using MRI reconstruction
as an example. Our method consistently outperforms conventional data-driven
techniques and traditional regularization approaches, excelling in both
reconstruction quality and robustness.