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Data-driven Methods in Inverse Problems
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).ORCID-id: 0000-0001-9928-3407
2019 (Engelska)Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
Abstract [en]

In this thesis on data-driven methods in inverse problems we introduce several new methods to solve inverse problems using recent advancements in machine learning and specifically deep learning. The main goal has been to develop practically applicable methods, scalable to medical applications and with the ability to handle all the complexities associated with them.

In total, the thesis contains six papers. Some of them are focused on more theoretical questions such as characterizing the optimal solutions of reconstruction schemes or extending current methods to new domains, while others have focused on practical applicability. A significant portion of the papers also aim to bringing knowledge from the machine learning community into the imaging community, with considerable effort spent on translating many of the concepts. The papers have been published in a range of venues: machine learning, medical imaging and inverse problems.

The first two papers contribute to a class of methods now called learned iterative reconstruction where we introduce two ways of combining classical model driven reconstruction methods with deep neural networks. The next two papers look forward, aiming to address the question of "what do we want?" by proposing two very different but novel loss functions for training neural networks in inverse problems. The final papers dwelve into the statistical side, one gives a generalization of a class of deep generative models to Banach spaces while the next introduces two ways in which such methods can be used to perform Bayesian inversion at scale.

Ort, förlag, år, upplaga, sidor
Stockholm: KTH Royal Institute of Technology, 2019. , s. 196
Serie
TRITA-SCI-FOU ; 2019;49
Nyckelord [en]
Inverse Problems, Machine Learning, Tomography
Nationell ämneskategori
Beräkningsmatematik
Identifikatorer
URN: urn:nbn:se:kth:diva-262727ISBN: 978-91-7873-334-7 (tryckt)OAI: oai:DiVA.org:kth-262727DiVA, id: diva2:1362355
Disputation
2019-10-31, F3, Lindstedtsvägen26, KTH, Stockholm, 14:00 (Engelska)
Opponent
Handledare
Forskningsfinansiär
Stiftelsen för strategisk forskning (SSF)Tillgänglig från: 2019-10-21 Skapad: 2019-10-18 Senast uppdaterad: 2019-10-21Bibliografiskt granskad
Delarbeten
1. Solving ill-posed inverse problems using iterative deep neural networks
Öppna denna publikation i ny flik eller fönster >>Solving ill-posed inverse problems using iterative deep neural networks
2017 (Engelska)Ingår i: Inverse Problems, ISSN 0266-5611, E-ISSN 1361-6420, Vol. 33, nr 12, artikel-id 124007Artikel i tidskrift (Refereegranskat) Published
Abstract [en]

We propose a partially learned approach for the solution of ill-posed inverse problems with not necessarily linear forward operators. The method builds on ideas from classical regularisation theory and recent advances in deep learning to perform learning while making use of prior information about the inverse problem encoded in the forward operator, noise model and a regularising functional. The method results in a gradient-like iterative scheme, where the 'gradient' component is learned using a convolutional network that includes the gradients of the data discrepancy and regulariser as input in each iteration. We present results of such a partially learned gradient scheme on a non-linear tomographic inversion problem with simulated data from both the Sheep-Logan phantom as well as a head CT. The outcome is compared against filtered backprojection and total variation reconstruction and the proposed method provides a 5.4 dB PSNR improvement over the total variation reconstruction while being significantly faster, giving reconstructions of 512 x 512 pixel images in about 0.4 s using a single graphics processing unit (GPU).

Ort, förlag, år, upplaga, sidor
Institute of Physics Publishing (IOPP), 2017
Nyckelord
tomography, deep learning, gradient descent, regularization
Nationell ämneskategori
Matematik
Identifikatorer
urn:nbn:se:kth:diva-219496 (URN)10.1088/1361-6420/aa9581 (DOI)000416015300001 ()2-s2.0-85038424472 (Scopus ID)
Anmärkning

QC 20171207

Tillgänglig från: 2017-12-07 Skapad: 2017-12-07 Senast uppdaterad: 2019-10-18Bibliografiskt granskad
2. Learned Primal-Dual Reconstruction
Öppna denna publikation i ny flik eller fönster >>Learned Primal-Dual Reconstruction
2018 (Engelska)Ingår i: IEEE Transactions on Medical Imaging, ISSN 0278-0062, E-ISSN 1558-254X, Vol. 37, nr 6, s. 1322-1332Artikel i tidskrift (Refereegranskat) Published
Abstract [en]

We propose the Learned Primal-Dual algorithm for tomographic reconstruction. The algorithm accounts for a (possibly non-linear) forward operator in a deep neural network by unrolling a proximal primal-dual optimization method, but where the proximal operators have been replaced with convolutional neural networks. The algorithm is trained end-to-end, working directly from raw measured data and it does not depend on any initial reconstruction such as filtered back-projection (FBP). We compare performance of the proposed method on low dose computed tomography reconstruction against FBP, total variation (TV), and deep learning based post-processing of FBP. For the Shepp-Logan phantom we obtain >6 dB peak signal to noise ratio improvement against all compared methods. For human phantoms the corresponding improvement is 6.6 dB over TV and 2.2 dB over learned post-processing along with a substantial improvement in the structural similarity index. Finally, our algorithm involves only ten forward-back-projection computations, making the method feasible for time critical clinical applications.

Ort, förlag, år, upplaga, sidor
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 2018
Nyckelord
Inverse problems, tomography, deep learning, primal-dual, optimization
Nationell ämneskategori
Datorseende och robotik (autonoma system)
Identifikatorer
urn:nbn:se:kth:diva-231206 (URN)10.1109/TMI.2018.2799231 (DOI)000434302700004 ()29870362 (PubMedID)2-s2.0-85041342868 (Scopus ID)
Anmärkning

QC 20180629

Tillgänglig från: 2018-06-29 Skapad: 2018-06-29 Senast uppdaterad: 2019-10-18Bibliografiskt granskad
3. Task adapted reconstruction for inverse problems
Öppna denna publikation i ny flik eller fönster >>Task adapted reconstruction for inverse problems
Visa övriga...
(Engelska)Manuskript (preprint) (Övrigt vetenskapligt)
Abstract [en]

The paper considers the problem of performing a task defined on a model parameter that is only observed indirectly through noisy data in an ill-posed inverse problem. A key aspect is to formalize the steps of reconstruction and task as appropriate estimators (non-randomized decision rules) in statistical estimation problems. The implementation makes use of (deep) neural networks to provide a differentiable parametrization of the family of estimators for both steps. These networks are combined and jointly trained against suitable supervised training data in order to minimize a joint differentiable loss function, resulting in an end-to-end task adapted reconstruction method. The suggested framework is generic, yet adaptable, with a plug-and-play structure for adjusting both the inverse problem and the task at hand. More precisely, the data model (forward operator and statistical model of the noise) associated with the inverse problem is exchangeable, e.g., by using neural network architecture given by a learned iterative method. Furthermore, any task that is encodable as a trainable neural network can be used. The approach is demonstrated on joint tomographic image reconstruction, classification and joint tomographic image reconstruction segmentation.

Nyckelord
Inverse problems, image reconstruction, tomography, deep learning, feature reconstruction, segmentation, classification, regularization
Nationell ämneskategori
Beräkningsmatematik
Forskningsämne
Tillämpad matematik och beräkningsmatematik, Numerisk analys
Identifikatorer
urn:nbn:se:kth:diva-262725 (URN)
Anmärkning

QC 20191021

Tillgänglig från: 2019-10-18 Skapad: 2019-10-18 Senast uppdaterad: 2019-10-21Bibliografiskt granskad
4. Learning to solve inverse problems using Wasserstein loss
Öppna denna publikation i ny flik eller fönster >>Learning to solve inverse problems using Wasserstein loss
(Engelska)Manuskript (preprint) (Övrigt vetenskapligt)
Abstract [en]

We propose using the Wasserstein loss for training in inverse problems. In particular, we consider a learned primal-dual reconstruction scheme for ill-posed inverse problems using the Wasserstein distance as loss function in the learning. This is motivated by miss-alignments in training data, which when using standard mean squared error loss could severely degrade reconstruction quality. We prove that training with the Wasserstein loss gives a reconstruction operator that correctly compensates for miss-alignments in certain cases, whereas training with the mean squared error gives a smeared reconstruction. Moreover, we demonstrate these effects by training a reconstruction algorithm using both mean squared error and optimal transport loss for a problem in computerized tomography.

Nationell ämneskategori
Beräkningsmatematik Signalbehandling Medicinsk bildbehandling Sannolikhetsteori och statistik
Forskningsämne
Matematik; Tillämpad matematik och beräkningsmatematik
Identifikatorer
urn:nbn:se:kth:diva-239723 (URN)
Forskningsfinansiär
Stiftelsen för strategisk forskning (SSF), AM13- 0049Stiftelsen för strategisk forskning (SSF), ID14-0055Vetenskapsrådet, 2014-5870
Anmärkning

QC 20181211

Tillgänglig från: 2018-11-30 Skapad: 2018-11-30 Senast uppdaterad: 2019-10-18Bibliografiskt granskad
5. Banach Wasserstein GAN
Öppna denna publikation i ny flik eller fönster >>Banach Wasserstein GAN
2018 (Engelska)Ingår i: Advances in Neural Information Processing Systems 31 (NIPS 2018) / [ed] Bengio, S Wallach, H Larochelle, H Grauman, K CesaBianchi, N Garnett, R, Neural Information Processing Systems (NIPS) , 2018Konferensbidrag, Publicerat paper (Refereegranskat)
Abstract [en]

Wasserstein Generative Adversarial Networks (WGANs) can be used to generate realistic samples from complicated image distributions. The Wasserstein metric used in WGANs is based on a notion of distance between individual images, which induces a notion of distance between probability distributions of images. So far the community has considered l(2) as the underlying distance. We generalize the theory of WGAN with gradient penalty to Banach spaces, allowing practitioners to select the features to emphasize in the generator. We further discuss the effect of some particular choices of underlying norms, focusing on Sobolev norms. Finally, we demonstrate a boost in performance for an appropriate choice of norm on CIFAR-10 and CelebA.

Ort, förlag, år, upplaga, sidor
Neural Information Processing Systems (NIPS), 2018
Serie
Advances in Neural Information Processing Systems, ISSN 1049-5258 ; 31
Nationell ämneskategori
Sannolikhetsteori och statistik
Identifikatorer
urn:nbn:se:kth:diva-249915 (URN)000461852001031 ()
Konferens
32nd Conference on Neural Information Processing Systems (NIPS), DEC 02-08, 2018, Montreal, Canada
Anmärkning

QC 20190426

Tillgänglig från: 2019-04-26 Skapad: 2019-04-26 Senast uppdaterad: 2019-10-18Bibliografiskt granskad
6. Deep Bayesian Inversion
Öppna denna publikation i ny flik eller fönster >>Deep Bayesian Inversion
(Engelska)Manuskript (preprint) (Övrigt vetenskapligt)
Abstract [en]

Characterizing statistical properties of solutions of inverse problems is essential for decision making. Bayesian inversion offers a tractable framework for this purpose, but current approaches are computationally unfeasible for most realistic imaging applications in the clinic. We introduce two novel deep learning based methods for solving large-scale inverse problems using Bayesian inversion: a sampling based method using a WGAN with a novel mini-discriminator and a direct approach that trains a neural network using a novel loss function. The performance of both methods is demonstrated on image reconstruction in ultra low dose 3D helical CT. We compute the posterior mean and standard deviation of the 3D images followed by a hypothesis test to assess whether a "dark spot" in the liver of a cancer stricken patient is present. Both methods are computationally efficient and our evaluation shows very promising performance that clearly supports the claim that Bayesian inversion is usable for 3D imaging in time critical applications.

Nationell ämneskategori
Beräkningsmatematik
Forskningsämne
Tillämpad matematik och beräkningsmatematik, Numerisk analys
Identifikatorer
urn:nbn:se:kth:diva-262726 (URN)
Anmärkning

QC 20191021

Tillgänglig från: 2019-10-18 Skapad: 2019-10-18 Senast uppdaterad: 2019-10-21Bibliografiskt granskad

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