Learned Regularizers for Inverse Problems

Lunz, Sebastian

doi:10.1007/978-3-030-98661-2_68

Cited by 29 publications

(56 citation statements)

References 21 publications

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“…6. (Left to Right) ground truth, reconstruction using Wavelet sparsity regularization, Adversarial Regularizer [24], postprocessing using UNet [18], UNet with FJA&FJ and UNet with SJA&SJ, postprocessing using UNet [18] regularized with SJA&SJ.…”

Section: Discussionmentioning

confidence: 99%

“…Finally there is also a new suite of techniques that leverage the knowledge of forward operator as follows: the reconstruction of the desired data vector given the measurements vector is carried out using a (regularized) optimization problem using the underlying model; however, the regularizer within such an optimization problem is itself learnt directly from a set of data examples. One such recent (unsupervised) approach relies on the use of adversarially learnt data dependent regularizers [24]. Another suite of techniques uses instead data representations learnt directly from data in any underlying model based optimization problem.…”

Section: Model-aware Data Driven Approachesmentioning

confidence: 99%

“…We also consider for comparison purposes competing techniques such as (a) wavelet sparsity regularized reconstruction [3]; (b) adversarial regularizers [24]; and (c) postprocessing via UNet method [18]. For a fair comparison, the UNet architecture and training routines are kept the same for our work and the postprocessing method.…”

Section: B Image Supermentioning

confidence: 99%

“…Note also that unlike [18], we train the post processing UNet on ℓ 2 loss function. For the Adversarial regularization method, we modify the official implementation of the adversarial regularizer, present on Github [24], provided by the authors of the publication to suit the forward model used in this work. The batch size and other hyperparameters such as the step size and the choice of the adversarial regularizer network were kept the same as in the original implementation.…”

Section: B Image Supermentioning

confidence: 99%

See 3 more Smart Citations

Deep Learning Model-Aware Regulatization With Applications to Inverse Problems

Amjad¹,

Lyu²,

Rodrigues³

2021

IEEE Trans. Signal Process.

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Section: Discussionmentioning

confidence: 99%

Section: Model-aware Data Driven Approachesmentioning

confidence: 99%

Section: B Image Supermentioning

confidence: 99%

Section: B Image Supermentioning

confidence: 99%

See 2 more Smart Citations

Deep Learning Model-Aware Regulatization With Applications to Inverse Problems

Amjad¹,

Lyu²,

Rodrigues³

2021

IEEE Trans. Signal Process.

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“…In this sense, the algorithm can be considered semi-supervised. This idea was followed, for example, in Lunz et al (2018), andLi et al (2020). Taking a Bayesian viewpoint, one can also learn prior distributions as deep NNs; this was done in Barbano et al (2020).…”

Section: Deep Neural Network Meet Inverse Problemsmentioning

confidence: 99%

The Modern Mathematics of Deep Learning

Berner¹,

Kutyniok²,

Petersen³

2022

Mathematical Aspects of Deep Learning

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We describe the new field of the mathematical analysis of deep learning. This field emerged around a list of research questions that were not answered within the classical framework of learning theory. These questions concern: the outstanding generalization power of overparametrized neural networks, the role of depth in deep architectures, the apparent absence of the curse of dimensionality, a surprisingly successful optimization performance despite the non-convexity of the problem, understanding what features are learned, why deep architectures perform exceptionally well in physical problems, and which fine aspects of an architecture affect the behavior of a learning task in which way. We present an overview of modern approaches that yield partial answers to these questions. For selected approaches, we describe the main ideas in more detail.Definition 1.4 (FC neural network). A fully connected feed-forward neural network is given by its architecture a = (N, ), where L ∈ N, N ∈ N L+1 , and : R → R. We refer to as the activation function, to L as the number of layers, and to N 0 , N L , and N , ∈ [L − 1], as the number of neurons in the input, output, and th hidden layer, respectively. We denote the number of parameters by

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End‐to‐end memory‐efficient reconstruction for cone beam CT

Moriakov,

Sonke,

Teuwen

2023

Medical Physics

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BackgroundCone beam computed tomography (CBCT) plays an important role in many medical fields nowadays. Unfortunately, the potential of this imaging modality is hampered by lower image quality compared to the conventional CT, and producing accurate reconstructions remains challenging. A lot of recent research has been directed towards reconstruction methods relying on deep learning, which have shown great promise for various imaging modalities. However, practical application of deep learning to CBCT reconstruction is complicated by several issues, such as exceedingly high memory costs of deep learning methods when working with fully 3D data. Additionally, deep learning methods proposed in the literature are often trained and evaluated only on data from a specific region of interest, thus raising concerns about possible lack of generalization to other regions.PurposeIn this work, we aim to address these limitations and propose LIRE: a learned invertible primal‐dual iterative scheme for CBCT reconstruction.MethodsLIRE is a learned invertible primal‐dual iterative scheme for CBCT reconstruction, wherein we employ a U‐Net architecture in each primal block and a residual convolutional neural network (CNN) architecture in each dual block. Memory requirements of the network are substantially reduced while preserving its expressive power through a combination of invertible residual primal‐dual blocks and patch‐wise computations inside each of the blocks during both forward and backward pass. These techniques enable us to train on data with isotropic 2 mm voxel spacing, clinically‐relevant projection count and detector panel resolution on current hardware with 24 GB video random access memory (VRAM).ResultsTwo LIRE models for small and for large field‐of‐view (FoV) setting were trained and validated on a set of 260 + 22 thorax CT scans and tested using a set of 142 thorax CT scans plus an out‐of‐distribution dataset of 79 head and neck CT scans. For both settings, our method surpasses the classical methods and the deep learning baselines on both test sets. On the thorax CT set, our method achieves peak signal‐to‐noise ratio (PSNR) of 33.84 ± 2.28 for the small FoV setting and 35.14 ± 2.69 for the large FoV setting; U‐Net baseline achieves PSNR of 33.08 ± 1.75 and 34.29 ± 2.71 respectively. On the head and neck CT set, our method achieves PSNR of 39.35 ± 1.75 for the small FoV setting and 41.21 ± 1.41 for the large FoV setting; U‐Net baseline achieves PSNR of 33.08 ± 1.75 and 34.29 ± 2.71 respectively. Additionally, we demonstrate that LIRE can be finetuned to reconstruct high‐resolution CBCT data with the same geometry but 1 mm voxel spacing and higher detector panel resolution, where it outperforms the U‐Net baseline as well.ConclusionsLearned invertible primal‐dual schemes with additional memory optimizations can be trained to reconstruct CBCT volumes directly from the projection data with clinically‐relevant geometry and resolution. Such methods can offer better reconstruction quality and generalization compared to classical deep learning baselines.

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Learned Regularizers for Inverse Problems

Cited by 29 publications

References 21 publications

Deep Learning Model-Aware Regulatization With Applications to Inverse Problems

Deep Learning Model-Aware Regulatization With Applications to Inverse Problems

The Modern Mathematics of Deep Learning

End‐to‐end memory‐efficient reconstruction for cone beam CT

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