Technology Category
Computer Vision: Learning & Optimization for CVSearch and Optimization: Non-convex OptimizationReasoning under Uncertainty: Stochastic Optimization
Learning Difference-of-Convex Regularizers for Inverse Problems: A Flexible Framework with Theoretical Guarantees
🤖 AI Summary
Ill-posed inverse problems—such as sparse-angle or limited-angle CT reconstruction—pose a fundamental challenge in balancing reconstruction performance and interpretability of regularization methods under small-data, weakly supervised regimes.
Method: We propose the first learnable Difference-of-Convex (DC) regularizer framework, introducing the DC structure into data-driven regularizer design for the first time. A deep neural network parameterizes the DC function, and optimization is efficiently performed via the Difference-of-Convex Algorithm (DCA) combined with proximal subgradient methods.
Contribution/Results: Theoretically, we establish a sufficient condition for a regularizer to admit a DC representation and rigorously prove the strong convergence of the proposed algorithm. Experimentally, our framework achieves state-of-the-art reconstruction accuracy under weak supervision, demonstrating both rigorous theoretical guarantees and superior empirical performance across multiple benchmarks.
Technology Category
Application Category
📝 Abstract
Learning effective regularization is crucial for solving ill-posed inverse problems, which arise in a wide range of scientific and engineering applications. While data-driven methods that parameterize regularizers using deep neural networks have demonstrated strong empirical performance, they often result in highly nonconvex formulations that lack theoretical guarantees. Recent work has shown that incorporating structured nonconvexity into neural network-based regularizers, such as weak convexity, can strike a balance between empirical performance and theoretical tractability. In this paper, we demonstrate that a broader class of nonconvex functions, difference-of-convex (DC) functions, can yield improved empirical performance while retaining strong convergence guarantees. The DC structure enables the use of well-established optimization algorithms, such as the Difference-of-Convex Algorithm (DCA) and a Proximal Subgradient Method (PSM), which extend beyond standard gradient descent. Furthermore, we provide theoretical insights into the conditions under which optimal regularizers can be expressed as DC functions. Extensive experiments on computed tomography (CT) reconstruction tasks show that our approach achieves strong performance across sparse and limited-view settings, consistently outperforming other weakly supervised learned regularizers. Our code is available at url{https://github.com/YasminZhang/ADCR}.
Problem
Research questions and friction points this paper is trying to address.
Regularization Methods
Performance and Reliability
Data Scarcity
Innovation
Methods, ideas, or system contributions that make the work stand out.
Differential Convex Functions
Regularization Technique
Sparse Data Reconstruction
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