Convex Latent-Optimized Adversarial Regularizers for Imaging Inverse Problems

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.