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Deep Injective Prior for Inverse Scattering
Machine Learning · Submitted 8 Jan 2023
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Extensive experiments with synthetic and experimental data demonstrate that our framework outperforms traditional iterative solvers, particularly for strong scatterers, while achieving comparable reconstruction quality to state-of-the-art supervised learning methods like the U-Net.
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The abstract, sentence by sentence
In electromagnetic inverse scattering, the goal is to reconstruct object permittivity using scattered waves. While deep learning has shown promise as an alternative to iterative solvers, it is primarily used in supervised frameworks which are sensitive to distribution drift of the scattered fields, common in practice. Moreover, these methods typically provide a single estimate of the permittivity pattern, which may be inadequate or misleading due to noise and the ill-posedness of the problem. In this paper, we propose a data-driven framework for inverse scattering based on deep generative models. Our approach learns a low-dimensional manifold as a regularizer for recovering target permittivities. Unlike supervised methods that necessitate both scattered fields and target permittivities, our method only requires the target permittivities for training; it can then be used with any experimental setup. We also introduce a Bayesian framework for approximating the posterior distribution of the target permittivity, enabling multiple estimates and uncertainty quantification. Extensive experiments with synthetic and experimental data demonstrate that our framework outperforms traditional iterative solvers, particularly for strong scatterers, while achieving comparable reconstruction quality to state-of-the-art supervised learning methods like the U-Net.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | In electromagnetic inverse scattering, the goal is to reconstruct object permittivity using scattered waves. | background 1.00 | 0.05 | 0.02 | asserted 1.00 |
| s1 | While deep learning has shown promise as an alternative to iterative solvers, it is primarily used in supervised frameworks which are sensitive to distribution drift of the scattered fields, common in practice. | background 0.59 | 0.06 | 0.02 | asserted 0.98 |
| s2 | Moreover, these methods typically provide a single estimate of the permittivity pattern, which may be inadequate or misleading due to noise and the ill-posedness of the problem. | gap 0.74 | 0.06 | 0.02 | hedged possibility 0.98 |
| s3 | In this paper, we propose a data-driven framework for inverse scattering based on deep generative models. | contribution 0.99 | 0.86 | 0.05 | asserted 0.99 |
| s4 | Our approach learns a low-dimensional manifold as a regularizer for recovering target permittivities. | method 0.91 | 0.89 | 0.05 | asserted 1.00 |
| s5 | Unlike supervised methods that necessitate both scattered fields and target permittivities, our method only requires the target permittivities for training; it can then be used with any experimental setup. | contribution 0.53 | 0.82 | 0.07 | asserted 0.99 |
| s6 | We also introduce a Bayesian framework for approximating the posterior distribution of the target permittivity, enabling multiple estimates and uncertainty quantification. | contribution 0.64 | 0.93 | 0.07 | asserted 1.00 |
| s7 | Extensive experiments with synthetic and experimental data demonstrate that our framework outperforms traditional iterative solvers, particularly for strong scatterers, while achieving comparable reconstruction quality to state-of-the-art supervised learning methods like the U-Net. | result 1.00 | 0.96 | 0.86 | asserted 1.00 |
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The paper
Original abstract
In electromagnetic inverse scattering, the goal is to reconstruct object permittivity using scattered waves. While deep learning has shown promise as an alternative to iterative solvers, it is primarily used in supervised frameworks which are sensitive to distribution drift of the scattered fields, common in practice. Moreover, these methods typically provide a single estimate of the permittivity pattern, which may be inadequate or misleading due to noise and the ill-posedness of the problem. In this paper, we propose a data-driven framework for inverse scattering based on deep generative models. Our approach learns a low-dimensional manifold as a regularizer for recovering target permittivities. Unlike supervised methods that necessitate both scattered fields and target permittivities, our method only requires the target permittivities for training; it can then be used with any experimental setup. We also introduce a Bayesian framework for approximating the posterior distribution of the target permittivity, enabling multiple estimates and uncertainty quantification. Extensive experiments with synthetic and experimental data demonstrate that our framework outperforms traditional iterative solvers, particularly for strong scatterers, while achieving comparable reconstruction quality to state-of-the-art supervised learning methods like the U-Net.
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What it cites · 9 sentences without a confident label
Contests 1 paper
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While GANs have been used as generative priors for inverse problems [ref] , they are unstable in training [ref] and result in local minima in iterative approaches [ref] .
Towards Principled Methods for Training Generative Adversarial Networks · Introduction · contest 0.73
Uses the method or tool of 1 paper
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We thus use the reparameterization trick [ref] , letting $z = z_MAP + σ_q ⊙t$, where $t ∼(0, I)$ and $⊙$ denotes the element-wise multiplication.
Auto-Encoding Variational Bayes · Posterior Modeling and Uncertainty Quantification · 1.00
Uses data or values from 1 paper
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We train the model on two synthetic large-scale datasets: 1) MNIST [ref] with 60000 training samples in the resolution $N = 32$, and 2) a more challenging dataset we generated comprising 60000 training samples with resolution $N = 64$ of overlapping ellipses used in [ref] .
Conditional Injective Flows for Bayesian Imaging · Computational Experiments · 0.95
Compares with 1 paper
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Unlike the supervised learning methods for inverse scattering [ref] , which rely on paired training sets of contrast and scattered fields ${(x^(i), y^(i))}_i = 1^N$, our framework is unsupervised, without the need for scattered fields during training.
Phaseless Microwave Imaging Of Dielectric Cylinders: An Artificial Neural Networks-Based Approach · MAP inference with Injective Flows for Inverse Scattering · 0.89
Cites as support 1 paper
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While this approach yields good reconstructions for objects with small and moderate permittivity, due to the non-linearity the quality of back-projections significantly drops in large permittivity leading to a drop in the reconstruction quality [ref] .
Conditional Injective Flows for Bayesian Imaging · Introduction · 0.99
Cites as background 6 papers
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Some studies [ref] have utilized scattered fields as the input of the neural network.
Conditional Injective Flows for Bayesian Imaging · Introduction · 0.82
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Further investigation on the universality of density and manifold approximation of injective flows can be found in [ref] .
Universal Joint Approximation of Manifolds and Densities by Simple Injective Flows · Injective Normalizing Flows · 0.95
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Deep generative models such as generative adversarial networks (GANs) [ref] , variational autoencoders (VAEs) [ref] , normalizing flows [ref] and diffusion models [ref] belong to a class of unsupervised learning methods and train a deep neural network to transform the samples of a simple (Gaussian) distribution into samples that resemble the target data distribution.
Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks · Introduction · 1.00
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