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  • 1.
    Adler, Jonas
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Data-driven Methods in Inverse Problems2019Doktorsavhandling, 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.

  • 2.
    Adler, Jonas
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Lunz, Sebastian
    Univ Cambridge, Dept Appl Math & Theoret Phys, Cambridge, England..
    Banach Wasserstein GAN2018Ingår 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 (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.

  • 3.
    Adler, Jonas
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.). Elekta.
    Lunz, Sebastian
    Centre for Mathematical Sciences, University of Cambridge, Cambridge CB3 0WA, United Kingdom.
    Verdier, Olivier
    Department of Mathematics, KTH Royal Institute of Technology, 100 44 Stockholm, Sweden ; Department of Computing, Mathematics and Physics, Western Norway University of Applied Sciences, Bergen, Norway.
    Schönlieb, Carola-Bibiane
    Centre for Mathematical Sciences, University of Cambridge, Cambridge CB3 0WA, United Kingdom.
    Öktem, Ozan
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Task adapted reconstruction for inverse problemsManuskript (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.

  • 4.
    Adler, Jonas
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.). Elekta, Box 7593, 103 93 Stockholm, Sweden.
    Ringh, Axel
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Öktem, Ozan
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Karlsson, Johan
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Learning to solve inverse problems using Wasserstein lossManuskript (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.

  • 5.
    Adler, Jonas
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.). Elekta.
    Öktem, Ozan
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Deep Bayesian InversionManuskript (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.

  • 6.
    Adler, Jonas
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.). Elekta Instrument AB, Stockholm, Sweden.
    Öktem, Ozan
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Learned Primal-Dual Reconstruction2018Ingår i: IEEE Transactions on Medical Imaging, ISSN 0278-0062, E-ISSN 1558-254X, Vol. 37, nr 6, s. 1322-1332Artikel i tidskrift (Refereegranskat)
    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.

  • 7.
    Adler, Jonas
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Öktem, Ozan
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Solving ill-posed inverse problems using iterative deep neural networks2017Ingår i: Inverse Problems, ISSN 0266-5611, E-ISSN 1361-6420, Vol. 33, nr 12, artikel-id 124007Artikel i tidskrift (Refereegranskat)
    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).

  • 8.
    Ashfaq, Awais
    et al.
    KTH. Halmstad University, Sweden.
    Adler, Jonas
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.). Elekta Instrument AB, Sweden.
    A modified fuzzy C means algorithm for shading correction in craniofacial CBCT images2017Ingår i: IFMBE Proceedings, Springer, 2017, s. 531-538Konferensbidrag (Refereegranskat)
    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.

  • 9.
    Banert, Sebastian
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Ringh, Axel
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Adler, Jonas
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.). Elekta, Box 7593, 103 93 Stockholm, Sweden.
    Karlsson, Johan
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Öktem, Ozan
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Data-driven nonsmooth optimizationManuskript (preprint) (Övrigt vetenskapligt)
  • 10.
    Hauptmann, Andreas
    et al.
    UCL, Dept Comp Sci, London WC1 6BT, England..
    Lucka, Felix
    UCL, Dept Comp Sci, London WC1 6BT, England.;Ctr Wiskunde & Informat, NL-1098 XG Amsterdam, Netherlands..
    Betcke, Marta
    UCL, Dept Comp Sci, London WC1 6BT, England..
    Huynh, Nam
    Adler, Jonas
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.). Elekta, S-10393 Stockholm, Sweden..
    Cox, Ben
    UCL, Dept Med Phys & Biomed Engn, London WC1 6BT, England..
    Beard, Paul
    UCL, Dept Med Phys & Biomed Engn, London WC1 6BT, England..
    Ourselin, Sebastien
    UCL, Dept Comp Sci, London WC1 6BT, England..
    Arridge, Simon
    UCL, Dept Comp Sci, London WC1 6BT, England..
    Model-Based Learning for Accelerated, Limited-View 3-D Photoacoustic Tomography2018Ingår i: IEEE Transactions on Medical Imaging, ISSN 0278-0062, E-ISSN 1558-254X, Vol. 37, nr 6, s. 1382-1393Artikel i tidskrift (Refereegranskat)
    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.

  • 11.
    Moriakov, Nikita
    et al.
    Radboud Univ Nijmegen, Med Ctr, Diagnost Image Anal Grp, Dept Radiol & Nucl Med, Nijmegen, Netherlands..
    Michielsen, Koen
    Radboud Univ Nijmegen, Med Ctr, Diagnost Image Anal Grp, Dept Radiol & Nucl Med, Nijmegen, Netherlands..
    Adler, Jonas
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.). Elekta, Res & Phys, Stockholm, Sweden..
    Mann, Ritse
    Radboud Univ Nijmegen, Med Ctr, Diagnost Image Anal Grp, Dept Radiol & Nucl Med, Nijmegen, Netherlands..
    Sechopoulos, Ioannis
    Radboud Univ Nijmegen, Med Ctr, Diagnost Image Anal Grp, Dept Radiol & Nucl Med, Nijmegen, Netherlands.;Dutch Expert Ctr Screening, Nijmegen, Netherlands..
    Teuwen, Jonas
    Radboud Univ Nijmegen, Med Ctr, Diagnost Image Anal Grp, Dept Radiol & Nucl Med, Nijmegen, Netherlands.;Delft Univ Technol, Imaging Phys Dept, Opt Res Grp, Delft, Netherlands..
    Deep Learning Framework for Digital Breast Tomosynthesis Reconstruction2019Ingår i: MEDICAL IMAGING 2019: PHYSICS OF MEDICAL IMAGING / [ed] Schmidt, TG Chen, GH Bosmans, H, SPIE-INT SOC OPTICAL ENGINEERING , 2019, artikel-id 1094804Konferensbidrag (Refereegranskat)
    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.

  • 12.
    Persson, Mats
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Fysik, Medicinsk bildfysik.
    Adler, Jonas
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Spectral CT reconstruction with anti-correlated noise model and joint prior2017Konferensbidrag (Övrigt vetenskapligt)
    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.

  • 13. Zhong, Z.
    et al.
    Palenstijn, W. J.
    Adler, Jonas
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.). Elekta, Stockholm, Sweden.
    Batenburg, K. J.
    EDS tomographic reconstruction regularized by total nuclear variation joined with HAADF-STEM tomography2018Ingår i: Ultramicroscopy, ISSN 0304-3991, E-ISSN 1879-2723, Vol. 191, s. 34-43Artikel i tidskrift (Refereegranskat)
    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.

1 - 13 av 13
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