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Adler, J. (2019). Data-driven Methods in Inverse Problems. (Doctoral dissertation). Stockholm: KTH Royal Institute of Technology
Open this publication in new window or tab >>Data-driven Methods in Inverse Problems
2019 (English)Doctoral thesis, comprehensive summary (Other academic)
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.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2019. p. 196
Series
TRITA-SCI-FOU ; 2019;49
Keywords
Inverse Problems, Machine Learning, Tomography
National Category
Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-262727 (URN)978-91-7873-334-7 (ISBN)
Public defence
2019-10-31, F3, Lindstedtsvägen26, KTH, Stockholm, 14:00 (English)
Opponent
Supervisors
Funder
Swedish Foundation for Strategic Research
Available from: 2019-10-21 Created: 2019-10-18 Last updated: 2019-10-21Bibliographically approved
Moriakov, N., Michielsen, K., Adler, J., Mann, R., Sechopoulos, I. & Teuwen, J. (2019). Deep Learning Framework for Digital Breast Tomosynthesis Reconstruction. In: Schmidt, TG Chen, GH Bosmans, H (Ed.), MEDICAL IMAGING 2019: PHYSICS OF MEDICAL IMAGING. Paper presented at Conference on Medical Imaging - Physics of Medical Imaging, FEB 17-20, 2019, San Diego, CA. SPIE-INT SOC OPTICAL ENGINEERING, Article ID 1094804.
Open this publication in new window or tab >>Deep Learning Framework for Digital Breast Tomosynthesis Reconstruction
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2019 (English)In: MEDICAL IMAGING 2019: PHYSICS OF MEDICAL IMAGING / [ed] Schmidt, TG Chen, GH Bosmans, H, SPIE-INT SOC OPTICAL ENGINEERING , 2019, article id 1094804Conference paper, Published paper (Refereed)
Abstract [en]

Digital breast tomosynthesis is rapidly replacing digital mammography as the basic x-ray technique for evaluation of the breasts. However, the sparse sampling and limited angular range gives rise to different artifacts, which manufacturers try to solve in several ways. In this study we propose an extension of the Learned Primal Dual algorithm for digital breast tomosynthesis. The Learned Primal-Dual algorithm is a deep neural network consisting of several 'reconstruction blocks', which take in raw sinogram data as the initial input, perform a forward and a backward pass by taking projections and back-projections, and use a convolutional neural network to produce an intermediate reconstruction result which is then improved further by the successive reconstruction block. We extend the architecture by providing breast thickness measurements as a mask to the neural network and allow it to learn how to use this thickness mask. We have trained the algorithm on digital phantoms and the corresponding noise-free/noisy projections, and then tested the algorithm on digital phantoms for varying level of noise. Reconstruction performance of the algorithms was compared visually, using MSE loss and Structural Similarity Index. Results indicate that the proposed algorithm outperforms the baseline iterative reconstruction algorithm in terms of reconstruction quality for both breast edges and internal structures and is robust to noise.

Place, publisher, year, edition, pages
SPIE-INT SOC OPTICAL ENGINEERING, 2019
Series
Proceedings of SPIE, ISSN 0277-786X ; 10948
Keywords
deep learning, digital breast tomosynthesis, primal-dual algorithm, breast cancer, reconstruction
National Category
Radiology, Nuclear Medicine and Medical Imaging
Identifiers
urn:nbn:se:kth:diva-260225 (URN)10.1117/12.2512912 (DOI)000483585700003 ()2-s2.0-85068378440 (Scopus ID)978-1-5106-2544-0 (ISBN)
Conference
Conference on Medical Imaging - Physics of Medical Imaging, FEB 17-20, 2019, San Diego, CA
Note

QC 20190930

Available from: 2019-09-30 Created: 2019-09-30 Last updated: 2019-09-30Bibliographically approved
Adler, J. & Lunz, S. (2018). Banach Wasserstein GAN. In: Bengio, S Wallach, H Larochelle, H Grauman, K CesaBianchi, N Garnett, R (Ed.), Advances in Neural Information Processing Systems 31 (NIPS 2018): . Paper presented at 32nd Conference on Neural Information Processing Systems (NIPS), DEC 02-08, 2018, Montreal, Canada. Neural Information Processing Systems (NIPS)
Open this publication in new window or tab >>Banach Wasserstein GAN
2018 (English)In: 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) , 2018Conference paper, Published paper (Refereed)
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.

Place, publisher, year, edition, pages
Neural Information Processing Systems (NIPS), 2018
Series
Advances in Neural Information Processing Systems, ISSN 1049-5258 ; 31
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:kth:diva-249915 (URN)000461852001031 ()
Conference
32nd Conference on Neural Information Processing Systems (NIPS), DEC 02-08, 2018, Montreal, Canada
Note

QC 20190426

Available from: 2019-04-26 Created: 2019-04-26 Last updated: 2019-10-18Bibliographically approved
Zhong, Z., Palenstijn, W. J., Adler, J. & Batenburg, K. J. (2018). EDS tomographic reconstruction regularized by total nuclear variation joined with HAADF-STEM tomography. Ultramicroscopy, 191, 34-43
Open this publication in new window or tab >>EDS tomographic reconstruction regularized by total nuclear variation joined with HAADF-STEM tomography
2018 (English)In: Ultramicroscopy, ISSN 0304-3991, E-ISSN 1879-2723, Vol. 191, p. 34-43Article in journal (Refereed) Published
Abstract [en]

Energy-dispersive X-ray spectroscopy (EDS) tomography is an advanced technique to characterize compositional information for nanostructures in three dimensions (3D). However, the application is hindered by the poor image quality caused by the low signal-to-noise ratios and the limited number of tilts, which are fundamentally limited by the insufficient number of X-ray counts. In this paper, we explore how to make accurate EDS reconstructions from such data. We propose to augment EDS tomography by joining with it a more accurate high-angle annular dark-field STEM (HAADF-STEM) tomographic reconstruction, for which usually a larger number of tilt images are feasible. This augmentation is realized through total nuclear variation (TNV) regularization, which encourages the joint EDS and HAADF reconstructions to have not only sparse gradients but also common edges and parallel (or antiparallel) gradients. Our experiments show that reconstruction images are more accurate compared to the non-regularized and the total variation regularized reconstructions, even when the number of tilts is small or the X-ray counts are low.

Place, publisher, year, edition, pages
Elsevier, 2018
National Category
Medical Image Processing
Identifiers
urn:nbn:se:kth:diva-228714 (URN)10.1016/j.ultramic.2018.04.011 (DOI)000436630300004 ()2-s2.0-85047082795 (Scopus ID)
Funder
Swedish Foundation for Strategic Research , ID14-0055
Note

QC 20180529

Available from: 2018-05-29 Created: 2018-05-29 Last updated: 2018-07-17Bibliographically approved
Adler, J. & Öktem, O. (2018). Learned Primal-Dual Reconstruction. IEEE Transactions on Medical Imaging, 37(6), 1322-1332
Open this publication in new window or tab >>Learned Primal-Dual Reconstruction
2018 (English)In: IEEE Transactions on Medical Imaging, ISSN 0278-0062, E-ISSN 1558-254X, Vol. 37, no 6, p. 1322-1332Article in journal (Refereed) 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.

Place, publisher, year, edition, pages
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 2018
Keywords
Inverse problems, tomography, deep learning, primal-dual, optimization
National Category
Computer Vision and Robotics (Autonomous Systems)
Identifiers
urn:nbn:se:kth:diva-231206 (URN)10.1109/TMI.2018.2799231 (DOI)000434302700004 ()29870362 (PubMedID)2-s2.0-85041342868 (Scopus ID)
Note

QC 20180629

Available from: 2018-06-29 Created: 2018-06-29 Last updated: 2019-10-18Bibliographically approved
Hauptmann, A., Lucka, F., Betcke, M., Huynh, N., Adler, J., Cox, B., . . . Arridge, S. (2018). Model-Based Learning for Accelerated, Limited-View 3-D Photoacoustic Tomography. IEEE Transactions on Medical Imaging, 37(6), 1382-1393
Open this publication in new window or tab >>Model-Based Learning for Accelerated, Limited-View 3-D Photoacoustic Tomography
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2018 (English)In: IEEE Transactions on Medical Imaging, ISSN 0278-0062, E-ISSN 1558-254X, Vol. 37, no 6, p. 1382-1393Article in journal (Refereed) Published
Abstract [en]

Recent advances in deep learning for tomographic reconstructions have shown great potential to create accurate and high quality images with a considerable speed up. In this paper, we present a deep neural network that is specifically designed to provide high resolution 3-D images from restricted photoacoustic measurements. The network is designed to represent an iterative scheme and incorporates gradient information of the data fit to compensate for limited view artifacts. Due to the high complexity of the photoacoustic forward operator, we separate training and computation of the gradient information. A suitable prior for the desired image structures is learned as part of the training. The resulting network is trained and tested on a set of segmented vessels from lung computed tomography scans and then applied to in-vivo photoacoustic measurement data.

Place, publisher, year, edition, pages
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 2018
Keywords
Deep learning, convolutional neural networks, photoacoustic tomography, iterative reconstruction
National Category
Medical Image Processing
Identifiers
urn:nbn:se:kth:diva-231207 (URN)10.1109/TMI.2018.2820382 (DOI)000434302700009 ()29870367 (PubMedID)2-s2.0-8504473367 (Scopus ID)
Note

QC 20180629

Available from: 2018-06-29 Created: 2018-06-29 Last updated: 2018-06-29Bibliographically approved
Ashfaq, A. & Adler, J. (2017). A modified fuzzy C means algorithm for shading correction in craniofacial CBCT images. In: IFMBE Proceedings: . Paper presented at International Conference on Medical and Biological Engineering, CMBEBIH 2017, 16 March 2017 through 18 March 2017 (pp. 531-538). Springer
Open this publication in new window or tab >>A modified fuzzy C means algorithm for shading correction in craniofacial CBCT images
2017 (English)In: IFMBE Proceedings, Springer, 2017, p. 531-538Conference paper, Published paper (Refereed)
Abstract [en]

CBCT images suffer from acute shading artifacts primarily due to scatter. Numerous image-domain correction algorithms have been proposed in the literature that use patient-specific planning CT images to estimate shading contributions in CBCT images. However, in the context of radiosurgery applications such as gamma knife, planning images are often acquired through MRI which impedes the use of polynomial fitting approaches for shading correction. We present a new shading correction approach that is independent of planning CT images. Our algorithm is based on the assumption that true CBCT images follow a uniform volumetric intensity distribution per material, and scatter perturbs this uniform texture by contributing cupping and shading artifacts in the image domain. The framework is a combination of fuzzy C-means coupled with a neighborhood regularization term and Otsu’s method. Experimental results on artificially simulated craniofacial CBCT images are provided to demonstrate the effectiveness of our algorithm. Spatial non-uniformity is reduced from 16% to 7% in soft tissue and from 44% to 8% in bone regions. With shading- correction, thresholding based segmentation accuracy for bone pixels is improved from 85% to 91% when compared to thresholding without shading-correction. The proposed algorithm is thus practical and qualifies as a p lug and p lay extension into any CBCT reconstruction software for shading correction.

Place, publisher, year, edition, pages
Springer, 2017
Keywords
Cone beam CT, Fuzzy C means, Shading correction, Biochemical engineering, Bone, Clustering algorithms, Copying, Fuzzy clustering, Fuzzy systems, Magnetic resonance imaging, Volumetric analysis, Cone-beam CT, Correction algorithms, Correction approaches, Fuzzy C mean, Fuzzy C-means algorithms, Intensity distribution, Reconstruction software, Segmentation accuracy, Computerized tomography
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-207385 (URN)10.1007/978-981-10-4166-2_81 (DOI)000462537100081 ()2-s2.0-85016072022 (Scopus ID)9789811041655 (ISBN)
Conference
International Conference on Medical and Biological Engineering, CMBEBIH 2017, 16 March 2017 through 18 March 2017
Note

QC 20170609

Available from: 2017-06-09 Created: 2017-06-09 Last updated: 2019-10-18Bibliographically approved
Persson, M. & Adler, J. (2017). Spectral CT reconstruction with anti-correlated noise model and joint prior. In: : . Paper presented at Proceedings of the 14th International Meeting on Fully Three-Dimensional Image Reconstruction in Radiology and Nuclear Medicine (pp. 580-585).
Open this publication in new window or tab >>Spectral CT reconstruction with anti-correlated noise model and joint prior
2017 (English)Conference paper, Published paper (Other academic)
Abstract [en]

Spectral CT allows reconstructing a set of material selective basis images which can be used for material quantification. These basis images can be reconstructed independently of each other or treated as a joint reconstruction problem. In this work, we investigate the effect of two ways of introducing coupling between the basis images: using an anti-correlated noise model and regularizing the basis images with a joint prior. We simulate imaging of a FORBILD Head phantom with an ideal photon-counting detector and reconstruct the resulting basis sinograms with and without these two kinds of coupling. The results show that the anti-correlated noise model gives better spatial resolution than the uncorrelated noise model at the same noise level, but also introduces artifacts. If anti-correlations are introduced also in the prior, these artifacts are reduced and the resolution is improved further.

National Category
Medical Image Processing
Identifiers
urn:nbn:se:kth:diva-250643 (URN)10.12059/Fully3D.2017-11-3203027 (DOI)
Conference
Proceedings of the 14th International Meeting on Fully Three-Dimensional Image Reconstruction in Radiology and Nuclear Medicine
Note

QC 20190520

Available from: 2019-05-01 Created: 2019-05-01 Last updated: 2019-05-20Bibliographically approved
Adler, J. & Öktem, O.Deep Bayesian Inversion.
Open this publication in new window or tab >>Deep Bayesian Inversion
(English)Manuscript (preprint) (Other academic)
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.

National Category
Computational Mathematics
Research subject
Applied and Computational Mathematics, Numerical Analysis
Identifiers
urn:nbn:se:kth:diva-262726 (URN)
Note

QC 20191021

Available from: 2019-10-18 Created: 2019-10-18 Last updated: 2019-10-21Bibliographically approved
Adler, J., Lunz, S., Verdier, O., Schönlieb, C.-B. & Öktem, O.Task adapted reconstruction for inverse problems.
Open this publication in new window or tab >>Task adapted reconstruction for inverse problems
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(English)Manuscript (preprint) (Other academic)
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.

Keywords
Inverse problems, image reconstruction, tomography, deep learning, feature reconstruction, segmentation, classification, regularization
National Category
Computational Mathematics
Research subject
Applied and Computational Mathematics, Numerical Analysis
Identifiers
urn:nbn:se:kth:diva-262725 (URN)
Note

QC 20191021

Available from: 2019-10-18 Created: 2019-10-18 Last updated: 2019-10-21Bibliographically approved
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0001-9928-3407

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