Papers › Learning Difference-of-Convex Regularizers for Inverse Problems: A Flexible Framework...

Learning Difference-of-Convex Regularizers for Inverse Problems: A Flexible Framework with Theoretical Guarantees

1 Feb 2025arXiv:2502.00240archive 2025-07-28

Yasi Zhang, Oscar Leong

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}.

PaperPDFCode

In Syntology Open this paper in Syntology's Atlas, the map of the papers in Syntology's graph and their citations.

Code

yasminzhang/adcr officialmentioned in papermentioned on GitHubpytorch report

Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.

Code Syntology ran Syntology

Not run by Syntology. Nothing on this page verifies that the listed code works.

Tasks

CT ReconstructionComputed Tomography (CT)

Results from the paper archive 2025-07-28

No leaderboard rows for this paper in the archive.

Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections