mlsanityData to 14 Oct 2026

Inverse Problems with Learned Forward Operators

arXiv 2311.12528 ↗First posted 21 Nov 2023math.NA cs.LG cs.NAcited by 4

Not on the map. Why?

Abstract (arXiv)

Solving inverse problems requires the knowledge of the forward operator, but accurate models can be computationally expensive and hence cheaper variants that do not compromise the reconstruction quality are desired. This chapter reviews reconstruction methods in inverse problems with learned forward operators that follow two different paradigms. The first one is completely agnostic to the forward operator and learns its restriction to the subspace spanned by the training data. The framework of regularisation by projection is then used to find a reconstruction. The second one uses a simplified model of the physics of the measurement process and only relies on the training data to learn a model correction. We present the theory of these two approaches and compare them numerically. A common theme emerges: both methods require, or at least benefit from, training data not only for the forward operator, but also for its adjoint.

Key facts. Cited by 4 papers in the map (data through 14 Oct 2026). Builds on 17 of its 68 references that are in the map. First posted on arXiv 21 Nov 2023.

Builds on

17 of 68 references.

References · 17

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5 more
  1. 2023Error Bounds for Learning with Vector-Valued Random Featurescited by 23
  2. 2019Meta-learning Pseudo-differential Operators with Deep Neural Networkscited by 17
  3. 2018Approximate k-space models and Deep Learning for fast photoacoustic reconstructioncited by 7
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  5. 2023Joint Activity Detection and Channel Estimation for Clustered Massive Machine Type Communicationscited by 1

Built on by

Cited by year (2026 to 14 Oct)

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

4 papers.

  1. 2024Physics-informed neural networks (PINNs) for numerical model error approximation and superresolutioncited by 0
  2. 2025Bayesian Model Parameter Learning in Linear Inverse Problems: Application in EEG Focal Source Imagingcited by 0
  3. 2025Evaluating structural uncertainty in accelerated MRI: are voxelwise measures useful surrogates?cited by 0
  4. 2026Uncertainty-quantified Pulse Signal Recovery from Facial Video using Regularized Stochastic Interpolantscited by 0