Task adapted reconstruction for inverse problems
| Autor: | Sebastian Lunz, Jonas Adler, Olivier Verdier, Ozan Öktem, Carola-Bibiane Schönlieb |
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| Přispěvatelé: | Adler, J [0000-0001-9928-3407], Schönlieb, CB [0000-0003-0099-6306], Öktem, O [0000-0002-1118-6483], Apollo - University of Cambridge Repository |
| Rok vydání: | 2022 |
| Předmět: |
Inverse problems
FOS: Computer and information sciences Computer Science - Machine Learning Beräkningsmatematik Computer Vision and Pattern Recognition (cs.CV) Computer Science - Computer Vision and Pattern Recognition tomography Machine Learning (cs.LG) Theoretical Computer Science Task (project management) FOS: Mathematics Noisy data Mathematical Physics Mathematics inverse problems Applied Mathematics Numerical analysis segmentation deep learning Computational mathematics Inverse problem image reconstruction Functional Analysis (math.FA) Computer Science Applications Mathematics - Functional Analysis regularization Computational Mathematics feature reconstruction Model parameter classification Signal Processing Key (cryptography) Algorithm |
| Zdroj: | Inverse Problems. 38:075006 |
| ISSN: | 1361-6420 0266-5611 |
| DOI: | 10.1088/1361-6420/ac28ec |
| Popis: | The paper considers the problem of performing a post-processing 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 post-processing 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 post-processing 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 post-processing that can be encoded as a trainable neural network can be used. The approach is demonstrated on joint tomographic image reconstruction, classification and joint tomographic image reconstruction segmentation. |
| Databáze: | OpenAIRE |
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