RECORD
Solving inverse problems with deep neural networks driven by sparse signal decomposition in a physics-based dictionary
Machine Learning · Submitted 16 Jul 2021
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Our method can handle generative forward models that are costly to evaluate and exhibits similar performance in accuracy and computation time as a fully-learned DNN, while maintaining high interpretability and being easier to train.
The compiled record
The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
Open the compiled record
The abstract, sentence by sentence
Deep neural networks (DNN) have an impressive ability to invert very complex models, i.e. to learn the generative parameters from a model's output. Once trained, the forward pass of a DNN is often much faster than traditional, optimization-based methods used to solve inverse problems. This is however done at the cost of lower interpretability, a fundamental limitation in most medical applications. We propose an approach for solving general inverse problems which combines the efficiency of DNN and the interpretability of traditional analytical methods. The measurements are first projected onto a dense dictionary of model-based responses. The resulting sparse representation is then fed to a DNN with an architecture driven by the problem's physics for fast parameter learning. Our method can handle generative forward models that are costly to evaluate and exhibits similar performance in accuracy and computation time as a fully-learned DNN, while maintaining high interpretability and being easier to train. Concrete results are shown on an example of model-based brain parameter estimation from magnetic resonance imaging (MRI).
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Deep neural networks (DNN) have an impressive ability to invert very complex models, i.e. to learn the generative parameters from a model's output. | background 1.00 | 0.06 | 0.04 | asserted 1.00 |
| s1 | Once trained, the forward pass of a DNN is often much faster than traditional, optimization-based methods used to solve inverse problems. | background 1.00 | 0.11 | 0.03 | asserted 0.91 |
| s2 | This is however done at the cost of lower interpretability, a fundamental limitation in most medical applications. | background 0.52 | 0.10 | 0.04 | asserted 1.00 |
| s3 | We propose an approach for solving general inverse problems which combines the efficiency of DNN and the interpretability of traditional analytical methods. | contribution 1.00 | 0.77 | 0.36 | asserted 0.99 |
| s4 | The measurements are first projected onto a dense dictionary of model-based responses. | method 1.00 | 0.64 | 0.03 | asserted 0.99 |
| s5 | The resulting sparse representation is then fed to a DNN with an architecture driven by the problem's physics for fast parameter learning. | method 1.00 | 0.68 | 0.08 | asserted 0.99 |
| s6 | Our method can handle generative forward models that are costly to evaluate and exhibits similar performance in accuracy and computation time as a fully-learned DNN, while maintaining high interpretability and being easier to train. | result 0.87 | 0.93 | 0.78 | asserted 0.94 |
| s7 | Concrete results are shown on an example of model-based brain parameter estimation from magnetic resonance imaging (MRI). | result 0.61 | 0.92 | 0.06 | asserted 1.00 |
What was examined, and what was not
- arXiv listing abstract v1
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
The paper
Original abstract
Deep neural networks (DNN) have an impressive ability to invert very complex models, i.e. to learn the generative parameters from a model's output. Once trained, the forward pass of a DNN is often much faster than traditional, optimization-based methods used to solve inverse problems. This is however done at the cost of lower interpretability, a fundamental limitation in most medical applications. We propose an approach for solving general inverse problems which combines the efficiency of DNN and the interpretability of traditional analytical methods. The measurements are first projected onto a dense dictionary of model-based responses. The resulting sparse representation is then fed to a DNN with an architecture driven by the problem's physics for fast parameter learning. Our method can handle generative forward models that are costly to evaluate and exhibits similar performance in accuracy and computation time as a fully-learned DNN, while maintaining high interpretability and being easier to train. Concrete results are shown on an example of model-based brain parameter estimation from magnetic resonance imaging (MRI).
Human review
How the literature uses it
What this paper does with the arXiv papers it cites
Discussion
Know something about this paper? Leave a comment, or highlight any passage above to comment on it.