mlsanityData to 7 Oct 2026

Stability of Data-Dependent Ridge-Regularization for Inverse Problems

arXiv 2406.12289 ↗First posted 18 Jun 2024math.OC cs.LGcited by 5

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Abstract (arXiv)

Theoretical guarantees for the robust solution of inverse problems have important implications for applications. To achieve both guarantees and high reconstruction quality, we propose learning a pixel-based ridge regularizer with a data-dependent and spatially varying regularization strength. For this architecture, we establish the existence of solutions to the associated variational problem and the stability of its solution operator. Further, we prove that the reconstruction forms a maximum-a-posteriori approach. Simulations for biomedical imaging and material sciences demonstrate that the approach yields high-quality reconstructions even if only a small instance-specific training set is available.

Key facts. Cited by 5 papers in the map (data through 7 Oct 2026). Builds on 35 of its 62 references that are in the map. First posted on arXiv 18 Jun 2024.

Builds on

35 of 62 references.

References · 35

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23 more
  1. 2020Total Deep Variation for Linear Inverse Problemscited by 53
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  3. 2022A Neural-Network-Based Convex Regularizer for Inverse Problemscited by 40
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Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 1; 2025: 2; 2026: 2.

5 papers.

  1. 2025Learning Regularization Functionals for Inverse Problems: A Comparative Studycited by 12
  2. 2025DEALing with Image Reconstruction: Deep Attentive Least Squarescited by 6
  3. 2024Iteratively Refined Image Reconstruction with Learned Attentive Regularizerscited by 3
  4. 2026Weakly Convex Ridge Regularization for 3D Non-Cartesian MRI Reconstructioncited by 1
  5. 2026A Stability Benchmark of Generative Regularizers for Inverse Problemscited by 1