NETT: Solving Inverse Problems with Deep Neural Networks

Li, Housen; Schwab, Johannes; Antholzer, Stephan; Haltmeier, Markus

doi:10.48550/arxiv.1803.00092

Cited by 19 publications

(29 citation statements)

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“…Evidence bound The idea is now to combine (10) and (12). Then, observe that minimizing the so-called (negative) evidence bound on the overall negative log-likelihood in ( 7) can be phrased as follows:…”

Section: A Maximum-likelihood (Ml) Perspectivementioning

confidence: 99%

“…With the emergence of deep learning, modern approaches for solving inverse problems have increasingly shifted towards data-driven reconstruction [5], which generally offers significantly superior reconstruction quality as compared to the traditional variational methods. Data-adaptive reconstruction methods can broadly be classified into two categories: (i) end-to-end trained over-parametrized models that either attempt to map the measured data to the true model parameter (such as AUTOMAP proposed in [18]), or remove artifacts from the output of an analytical reconstruction method [10], and (ii) learning the image prior using a neural network based on training data of images and then using such a learned regularizer in a variational model for reconstruction [11,12,14,16]. The first approach relies on learning the reconstruction method from a large training dataset that consists of many ordered pairs of model-parameter and corresponding noisy data.…”

Section: Introductionmentioning

confidence: 99%

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Adversarially learned iterative reconstruction for imaging inverse problems

Mukherjee¹,

Öktem²,

Schönlieb³

2021

Preprint

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In numerous practical applications, especially in medical image reconstruction, it is often infeasible to obtain a large ensemble of ground-truth/measurement pairs for supervised learning. Therefore, it is imperative to develop unsupervised learning protocols that are competitive with supervised approaches in performance. Motivated by the maximum-likelihood principle, we propose an unsupervised learning framework for solving ill-posed inverse problems. Instead of seeking pixel-wise proximity between the reconstructed and the ground-truth images, the proposed approach learns an iterative reconstruction network whose output matches the ground-truth in distribution. Considering tomographic reconstruction as an application, we demonstrate that the proposed unsupervised approach not only performs on par with its supervised variant in terms of objective quality measures, but also successfully circumvents the issue of over-smoothing that supervised approaches tend to suffer from. The improvement in reconstruction quality comes at the expense of higher training complexity, but, once trained, the reconstruction time remains the same as its supervised counterpart.

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Section: A Maximum-likelihood (Ml) Perspectivementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Adversarially learned iterative reconstruction for imaging inverse problems

Mukherjee¹,

Öktem²,

Schönlieb³

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…The PDE is based on fundamental physical laws but the regulariser is more heuristic in nature. A number of recent works have employed deep learning to build regularisers for inverse problems, especially for seismic inversion [13,24,27] and medical imaging [17,14,2]. External operators in UFL provide a high-level programming abstraction for this problem.…”

Section: Example: Seismic Inversionmentioning

confidence: 99%

Escaping the abstraction: a foreign function interface for the Unified Form Language [UFL]

Bouziani¹,

Ham²

2021

Preprint

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High level domain specific languages for the finite element method underpin high productivity programming environments for simulations based on partial differential equations (PDE) while employing automatic code generation to achieve high performance. However, a limitation of this approach is that it does not support operators that are not directly expressible in the vector calculus. This is critical in applications where PDEs are not enough to accurately describe the physical problem of interest. The use of deep learning techniques have become increasingly popular in filling this knowledge gap, for example to include features not represented in the differential equations, or closures for unresolved spatiotemporal scales. We introduce an interface within the Firedrake finite element system that enables a seamless interface with deep learning models. This new feature composes with the automatic differentiation capabilities of Firedrake, enabling the automated solution of inverse problems. Our implementation interfaces with PyTorch and can be extended to other machine learning libraries. The resulting framework supports complex models coupling PDEs and deep learning whilst maintaining separation of concerns between application scientists and software experts.

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“…Traditionally, analytical methods, like filtered back-projection (FBP), or iterative reconstruction (IR) techniques are used for this task. Recently, image reconstruction approaches involving Deep Learning (DL) have been developed and demonstrated to be very competitive [4,9,18,22,23,30,34,37].…”

Section: Introductionmentioning

confidence: 99%

The LoDoPaB-CT Dataset: A Benchmark Dataset for Low-Dose CT Reconstruction Methods

Leuschner,

Schmidt,

Baguer

et al. 2019

Preprint

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Deep Learning approaches for solving Inverse Problems in imaging have become very effective and are demonstrated to be quite competitive in the field. Comparing these approaches is a challenging task since they highly rely on the data and the setup that is used for training. We provide a public dataset of computed tomography images and simulated low-dose measurements suitable for training this kind of methods. With the LoDoPaB-CT Dataset we aim to create a benchmark that allows for a fair comparison. It contains over 40 000 scan slices from around 800 patients selected from the LIDC/IDRI Database. In this paper we describe how we processed the original slices and how we simulated the measurements. We also include first baseline results.

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NETT: Solving Inverse Problems with Deep Neural Networks

Cited by 19 publications

References 0 publications

Adversarially learned iterative reconstruction for imaging inverse problems

Adversarially learned iterative reconstruction for imaging inverse problems

Escaping the abstraction: a foreign function interface for the Unified Form Language [UFL]

The LoDoPaB-CT Dataset: A Benchmark Dataset for Low-Dose CT Reconstruction Methods

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