Multi-Scale Learned Iterative Reconstruction

Hauptmann, Andreas; Adler, Jonas; Arridge, Simon; Öktem, Ozan

doi:10.1109/tci.2020.2990299

Cited by 36 publications

(28 citation statements)

References 42 publications

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“…In particular, we are motivated by model-based learned iterative reconstruction techniques that have shown to be highly successful in a variety of application areas [1,2,17,21,35]. These methods generally mimic iterative gradient descent schemes and demonstrate impressive reconstruction results with often considerable speed ups [18], but are mostly empirically motivated and lack convergence guarantees. In contrast, this paper follows a recent development of understanding how deep learning methods can be combined with classical reconstruction algorithms, such as variational techniques, and retaining established theoretical results on convergence.…”

Section: Introductionmentioning

confidence: 99%

On Learned Operator Correction in Inverse Problems

Lunz¹,

Hauptmann²,

Tarvainen³

et al. 2020

Preprint

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We discuss the possibility to learn a data-driven explicit model correction for inverse problems and whether such a model correction can be used within a variational framework to obtain regularised reconstructions. This paper discusses the conceptual difficulty to learn such a forward model correction and proceeds to present a possible solution as forward-backward correction that explicitly corrects in both data and solution spaces. We then derive conditions under which solutions to the variational problem with a learned correction converge to solutions obtained with the correct operator. The proposed approach is evaluated on an application to limited view photoacoustic tomography and compared to the established framework of Bayesian approximation error method.

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Section: Introductionmentioning

confidence: 99%

On Learned Operator Correction in Inverse Problems

Lunz¹,

Hauptmann²,

Tarvainen³

et al. 2020

Preprint

Self Cite

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“…where J(σ) is the Jacobian of the simulated voltages U (σ) (e.g., computed by [34], [35]). In Newton's method, the Hessian is computed exactly according to (11). In the Gauss-Newton (GN) method, the second term is ignored due to the costly computation of the second order derivative U i (σ).…”

Section: B the Inverse Problem For Eitmentioning

confidence: 99%

Graph Convolutional Networks for Model-Based Learning in Nonlinear Inverse Problems

Herzberg

Rowe

Hauptmann

et al. 2021

IEEE Trans. Comput. Imaging

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The majority of model-based learned image reconstruction methods in medical imaging have been limited to uniform domains, such as pixelated images. If the underlying model is solved on nonuniform meshes, arising from a finite element method typical for nonlinear inverse problems, interpolation and embeddings are needed. To overcome this, we present a flexible framework to extend model-based learning directly to nonuniform meshes, by interpreting the mesh as a graph and formulating our network architectures using graph convolutional neural networks. This gives rise to the proposed iterative Graph Convolutional Newton-type Method (GCNM), which includes the forward model in the solution of the inverse problem, while all updates are directly computed by the network on the problem specific mesh. We present results for Electrical Impedance Tomography, a severely ill-posed nonlinear inverse problem that is frequently solved via optimization-based methods, where the forward problem is solved by finite element methods. Results for absolute EIT imaging are compared to standard iterative methods as well as a graph residual network. We show that the GCNM has strong generalizability to different domain shapes and meshes, out of distribution data as well as experimental data, from purely simulated training data and without transfer training.

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“…Another idea of how to scale learned iterative schemes to 3D is by computing the forward model on multiple lower resolutions in the reconstruction process. 171…”

Section: D Nature Of Patmentioning

confidence: 99%

Deep learning in photoacoustic tomography: current approaches and future directions

2020

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Biomedical photoacoustic tomography, which can provide high-resolution 3D soft tissue images based on optical absorption, has advanced to the stage at which translation from the laboratory to clinical settings is becoming possible. The need for rapid image formation and the practical restrictions on data acquisition that arise from the constraints of a clinical workflow are presenting new image reconstruction challenges. There are many classical approaches to image reconstruction, but ameliorating the effects of incomplete or imperfect data through the incorporation of accurate priors is challenging and leads to slow algorithms. Recently, the application of deep learning (DL), or deep neural networks, to this problem has received a great deal of attention. We review the literature on learned image reconstruction, summarizing the current trends and explain how these approaches fit within, and to some extent have arisen from, a framework that encompasses classical reconstruction methods. In particular, it shows how these techniques can be understood from a Bayesian perspective, providing useful insights. We also provide a concise tutorial demonstration of three prototypical approaches to learned image reconstruction. The code and data sets for these demonstrations are available to researchers. It is anticipated that it is in in vivo applications-where data may be sparse, fast imaging critical, and priors difficult to construct by hand-that DL will have the most impact. With this in mind, we conclude with some indications of possible future research directions. © The Authors. Published by SPIE under a Creative Commons Attribution 4.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI.

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Multi-Scale Learned Iterative Reconstruction

Cited by 36 publications

References 42 publications

On Learned Operator Correction in Inverse Problems

On Learned Operator Correction in Inverse Problems

Graph Convolutional Networks for Model-Based Learning in Nonlinear Inverse Problems

Deep learning in photoacoustic tomography: current approaches and future directions

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