Convex Latent-Optimized Adversarial Regularizers for Imaging Inverse Problems

TL;DR

This paper introduces CLEAR, an interpretable and convex regularization framework combining deep learning and variational methods, which improves MRI reconstruction quality and robustness over existing techniques.

Contribution

CLEAR is a novel convex regularizer learned via latent optimization of an input convex neural network, ensuring interpretability, convergence, and robustness in imaging inverse problems.

Findings

Outperforms traditional regularization methods in MRI reconstruction

Guarantees convergence to a unique solution under certain conditions

Demonstrates stable reconstruction even with measurement interference

Abstract

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.