mlsanityData to 7 Oct 2026

Stability of Image-Reconstruction Algorithms

arXiv 2206.07128 ↗First posted 14 Jun 2022math.OC cs.LG eess.IVcited by 7

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Abstract (arXiv)

Robustness and stability of image-reconstruction algorithms have recently come under scrutiny. Their importance to medical imaging cannot be overstated. We review the known results for the topical variational regularization strategies (ℓ2 and ℓ1 regularization) and present novel stability results for ℓp-regularized linear inverse problems for p∈(1,∞). Our results guarantee Lipschitz continuity for small p and H"older continuity for larger p. They generalize well to the Lp(Omega) function spaces.

Key facts. Cited by 7 papers in the map (data through 7 Oct 2026). Builds on 19 of its 65 references that are in the map. First posted on arXiv 14 Jun 2022.

Builds on

19 of 65 references.

References · 19

  1. 2016Deep Convolutional Neural Network for Inverse Problems in Imagingcited by 431
  2. 2017Image reconstruction by domain transform manifold learningcited by 231
  3. 2019On instabilities of deep learning in image reconstruction - Does AI come at a cost?cited by 211
  4. 2020Solving Inverse Problems With Deep Neural Networks -- Robustness Included?cited by 58
  5. 2021Measuring Robustness in Deep Learning Based Compressive Sensingcited by 53
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  7. 2018A representer theorem for deep neural networkscited by 38
  8. 2020Stabilizing Invertible Neural Networks Using Mixture Modelscited by 30
  9. 2018Sparsity of solutions for variational inverse problems with finite-dimensional datacited by 25
  10. 2018On Representer Theorems and Convex Regularizationcited by 24
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  12. 2021Convex Optimization in Sums of Banach Spacescited by 11
7 more
  1. 2017Indirect Image Registration with Large Diffeomorphic Deformationscited by 4
  2. 2018Template-Based Image Reconstruction from Sparse Tomographic Datacited by 3
  3. 2017Exact solutions of infinite dimensional total-variation regularized problemscited by 2
  4. 2017Cell Detection by Functional Inverse Diffusion and Non-negative Group Sparsity-Part II: Proximal Optimization and Performance Evaluationcited by 2
  5. 2015A unified approach to convergence rates for ℓ1-regularization and lacking sparsitycited by 1
  6. 2017Cell Detection by Functional Inverse Diffusion and Non-negative Group Sparsity-Part I: Modeling and Inverse Problemscited by 1
  7. 2018SpotNet - Learned iterations for cell detection in image-based immunoassayscited by 1

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 1; 2024: 4; 2025: 1; 2026: 1.

7 papers.

  1. 2023Conditional Generative Models are Provably Robust: Pointwise Guarantees for Bayesian Inverse Problemscited by 12
  2. 2024Stability of Data-Dependent Ridge-Regularization for Inverse Problemscited by 5
  3. 2024Iteratively Refined Image Reconstruction with Learned Attentive Regularizerscited by 3
  4. 2024Parseval Convolution Operators and Neural Networkscited by 2
  5. 2024Robustness and Exploration of Variational and Machine Learning Approaches to Inverse Problems: An Overviewcited by 1
  6. 2025Universal Architectures for the Learning of Polyhedral Norms and Convex Regularizerscited by 1
  7. 2026Triggering hallucinations in model-based MRI reconstruction via adversarial perturbationscited by 0