mlsanityData to 14 Oct 2026

Learning Regularization Functionals for Inverse Problems: A Comparative Study

arXiv 2510.01755 ↗First posted 2 Oct 2025cs.LG cs.NA math.NAcited by 15

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Abstract (arXiv)

In recent years, a variety of learned regularization frameworks for solving inverse problems in imaging have emerged. These offer flexible modeling together with mathematical insights. The proposed methods differ in their architectural design and training strategies, making direct comparison challenging due to non-modular implementations. We address this gap by collecting and unifying the available code into a common framework. This unified view allows us to systematically compare the approaches and highlight their strengths and limitations, providing valuable insights into their future potential. We also provide concise descriptions of each method, complemented by practical guidelines.

Key facts. Cited by 15 papers in the map (data through 14 Oct 2026). Builds on 98 of its 165 references that are in the map. First posted on arXiv 2 Oct 2025.

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98 of 165 references.

References · 98

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Citing papers per year: 2025: 2; 2026: 13.

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  1. 2025Nonasymptotic Convergence Rates for Plug-and-Play Methods With MMSE Denoiserscited by 2
  2. 2026A Stability Benchmark of Generative Regularizers for Inverse Problemscited by 2
  3. 2025Graph Neural Regularizers for PDE Inverse Problemscited by 1
  4. 2026Weakly Convex Ridge Regularization for 3D Non-Cartesian MRI Reconstructioncited by 1
  5. 2026Riemannian Archetypal Analysis: Interpretable non-linear data analysis on deformed star distributionscited by 1
  6. 2026Data-Consistent Learning of Inverse Problemscited by 0
  7. 2026Monotone Optimisation with Learned Projectionscited by 0
  8. 2026Diffusion Graph Posterior Sampling for Nonlinear Inverse Problems with Application to Electrical Impedance Tomographycited by 0
  9. 2026Self-Tuning Regularization for Image Scanning Microscopycited by 0
  10. 2026A Distributionally Robust Framework for Learned Reconstructions in Inverse Problemscited by 0
  11. 2026Learning spatially varying regularisation parameters of low regularity for image reconstructioncited by 0
  12. 2026CLEAR: Complex Learned Explicit Analytical Regularization for Ultra-Accelerated 4D Flow CMR Reconstructioncited by 0
3 more
  1. 2026Latent Score-Based Bayesian Cram'er-Rao Bound Estimation for High-Dimensional Imaging Systemscited by 0
  2. 2026The Geometry of Anisotropic Dilation for Optimal Regularizationcited by 0
  3. 2026Taming Nonconvexity with Epigraph Liftingcited by 0