# Task adapted reconstruction for inverse problems

arXiv: https://arxiv.org/abs/1809.00948 · HTML: https://mlsanity.com/paper/1809.00948/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Aug 2018.

## Built on by (most cited first, 16 of 16)

- [Reliable amortized variational inference with physics-based latent distribution correction](https://mlsanity.com/paper/2207.11640/) (2022)
- [Regularising Inverse Problems with Generative Machine Learning Models](https://mlsanity.com/paper/2107.11191/) (2021)
- [A study of why we need to reassess full reference image quality assessment with medical images](https://mlsanity.com/paper/2405.19097/) (2024)
- [Amortized Normalizing Flows for Transcranial Ultrasound with Uncertainty Quantification](https://mlsanity.com/paper/2303.03478/) (2023)
- [Deep Microlocal Reconstruction for Limited-Angle Tomography](https://mlsanity.com/paper/2108.05732/) (2021)
- [Stochastic Primal-Dual Deep Unrolling](https://mlsanity.com/paper/2110.10093/) (2021)
- [Balanced conic rectified flow](https://mlsanity.com/paper/2510.25229/) (2025)
- [Joint reconstruction-segmentation on graphs](https://mlsanity.com/paper/2208.05834/) (2022)
- [ATOMMIC: An Advanced Toolbox for Multitask Medical Imaging Consistency to facilitate Artificial Intelligence applications from acquisition to analysis in Magnetic Resonance Imaging](https://mlsanity.com/paper/2404.19665/) (2024)
- [Self-Supervised Denoiser Framework](https://mlsanity.com/paper/2411.19593/) (2024)
- [Geometric Autoencoder Priors for Bayesian Inversion: Learn First Observe Later](https://mlsanity.com/paper/2509.19929/) (2025)
- [A Note on Machine Learning Approach for Computational Imaging](https://mlsanity.com/paper/2202.11883/) (2022)
- [Statistical Component Separation for Targeted Signal Recovery in Noisy Mixtures](https://mlsanity.com/paper/2306.15012/) (2023)
- [Sparse View Tomographic Reconstruction of Elongated Objects using Learned Primal-Dual Networks](https://mlsanity.com/paper/2403.02820/) (2024)
- [Survey of Deep Learning and Physics-Based Approaches in Computational Wave Imaging](https://mlsanity.com/paper/2410.08329/) (2024)
- [Task-Adaptive Low-Dose CT Reconstruction](https://mlsanity.com/paper/2511.07094/) (2025)

## Abstract (arXiv)

The paper considers the problem of performing a task defined on a model parameter that is only observed indirectly through noisy data in an ill-posed inverse problem. A key aspect is to formalize the steps of reconstruction and task as appropriate estimators (non-randomized decision rules) in statistical estimation problems. The implementation makes use of (deep) neural networks to provide a differentiable parametrization of the family of estimators for both steps. These networks are combined and jointly trained against suitable supervised training data in order to minimize a joint differentiable loss function, resulting in an end-to-end task adapted reconstruction method. The suggested framework is generic, yet adaptable, with a plug-and-play structure for adjusting both the inverse problem and the task at hand. More precisely, the data model (forward operator and statistical model of the noise) associated with the inverse problem is exchangeable, e.g., by using neural network architecture given by a learned iterative method. Furthermore, any task that is encodable as a trainable neural network can be used. The approach is demonstrated on joint tomographic image reconstruction, classification and joint tomographic image reconstruction segmentation.