Deep null space learning for inverse problems: convergence analysis and rates

Schwab, Johannes; Antholzer, Stephan; Haltmeier, Markus

doi:10.1088/1361-6420/aaf14a

Cited by 82 publications

(96 citation statements)

References 32 publications

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“…More precisely, let A † : Y → X be an analytically known reconstruction operator that is proven to be robust. One can then train a convolutional neural network to remove reconstruction artefacts that arise from using A † [14], [15], [26]. These artefacts can be quite notable when data is highly noisy or under-sampled.…”

Section: A Reconstruction and Post-processingmentioning

confidence: 99%

Multi-Scale Learned Iterative Reconstruction

Hauptmann

Adler

Arridge

et al. 2020

IEEE Trans. Comput. Imaging

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Model-based learned iterative reconstruction methods have recently been shown to outperform classical reconstruction methods. Applicability of these methods to large scale inverse problems is however limited by the available memory for training and extensive training times. As a possible solution to these restrictions we propose a multi-scale learned iterative reconstruction algorithm that computes iterates on discretisations of increasing resolution. This procedure does not only reduce memory requirements, it also considerably speeds up reconstruction and training times, but most importantly is scalable to large scale inverse problems, like those that arise in 3D tomographic imaging. Feasibility of the proposed method to speed up training and computation times in comparison to established learned reconstruction methods in 2D is demonstrated for low dose computed tomography (CT), for which we utilise the data base of abdominal CT scans provided for the 2016 AAPM lowdose CT grand challenge. * Equal contribution.A. Hauptmann is with the Research

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Section: A Reconstruction and Post-processingmentioning

confidence: 99%

Multi-Scale Learned Iterative Reconstruction

Hauptmann

Adler

Arridge

et al. 2020

IEEE Trans. Comput. Imaging

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“…In this work, we compare the performance of the joint`1-minimization algorithm of [1] with deep learning approaches for CS PAT image reconstruction. For the latter we use the residual network [13,20,21] and the nullspace network [22,23]. The nullspace network includes a certain data consistency layer and even has been shown to be a regularization method in [23].…”

Section: Cs Pat Recovery Algorithmsmentioning

confidence: 99%

“…For the latter we use the residual network [13,20,21] and the nullspace network [22,23]. The nullspace network includes a certain data consistency layer and even has been shown to be a regularization method in [23]. Our results show that the nullspace network uniformly outperforms the residual network for CS PAT in terms of the mean squared error (MSE).…”

Section: Cs Pat Recovery Algorithmsmentioning

confidence: 99%

Deep Learning Versus <tex>$\ell^{1}$</tex> -Minimization for Compressed Sensing Photoacoustic Tomography

Antholzer

Schwab

Haltmeier

2018

2018 IEEE International Ultrasonics Symposium (IUS)

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We investigate compressed sensing (CS) techniques for reducing the number of measurements in photoacoustic tomography (PAT). High resolution imaging from CS data requires particular image reconstruction algorithms. The most established reconstruction techniques for that purpose use sparsity and`1-minimization. Recently, deep learning appeared as a new paradigm for CS and other inverse problems. In this paper, we compare a recently invented joint`1-minimization algorithm with two deep learning methods, namely a residual network and an approximate nullspace network. We present numerical results showing that all developed techniques perform well for deterministic sparse measurements as well as for random Bernoulli measurements. For the deterministic sampling, deep learning shows more accurate results, whereas for Bernoulli measurements thè 1 -minimization algorithm performs best. Comparing the implemented deep learning approaches, we show that the nullspace network uniformly outperforms the residual network in terms of the mean squared error (MSE).

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“…Recently, deep learning has achieved impressive results in various CT reconstruction fields [6], including low-dose denoising [7,8,9], sparse-view reconstruction [10], limited angle tomography [11], and metal artifact reduction [12]. In the field of interior tomography, Han and Ye applied the U-Net to remove null space artifacts [13] from FBP reconstruction. Observing its instability, they propose to use DBP reconstruction instead of the FBP reconstruction as the input of the U-Net for various types of ROI reconstruction tasks [14].…”

Section: Introductionmentioning

confidence: 99%

Field of View Extension in Computed Tomography Using Deep Learning Prior

et al. 2020

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In computed tomography (CT), data truncation is a common problem. Images reconstructed by the standard filtered back-projection algorithm from truncated data suffer from cupping artifacts inside the field-of-view (FOV), while anatomical structures are severely distorted or missing outside the FOV. Deep learning, particularly the U-Net, has been applied to extend the FOV as a post-processing method. Since image-toimage prediction neglects the data fidelity to measured projection data, incorrect structures, even inside the FOV, might be reconstructed by such an approach. Therefore, generating reconstructed images directly from a post-processing neural network is inadequate. In this work, we propose a data consistent reconstruction method, which utilizes deep learning reconstruction as prior for extrapolating truncated projections and a conventional iterative reconstruction to constrain the reconstruction consistent to measured raw data. Its efficacy is demonstrated in our study, achieving small average root-mean-square error of 24 HU inside the FOV and a high structure similarity index of 0.993 for the whole body area on a test patient's CT data.

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Deep null space learning for inverse problems: convergence analysis and rates

Cited by 82 publications

References 32 publications

Multi-Scale Learned Iterative Reconstruction

Multi-Scale Learned Iterative Reconstruction

Deep Learning Versus <tex>$\ell^{1}$</tex> -Minimization for Compressed Sensing Photoacoustic Tomography

Field of View Extension in Computed Tomography Using Deep Learning Prior

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