| 1. |
- Moriakov, Nikita, et al.
(författare)
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Deep Learning Framework for Digital Breast Tomosynthesis Reconstruction
- 2019
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Ingår i: MEDICAL IMAGING 2019. - : SPIE-INT SOC OPTICAL ENGINEERING. - 9781510625440
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Konferensbidrag (refereegranskat)abstract
- 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.
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| 2. |
- Moriakov, Nikita, et al.
(författare)
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Kernel of CycleGAN as a principle homogeneous space
- 2020
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Ingår i: 8th International Conference on Learning Representations, ICLR 2020. - : International Conference on Learning Representations, ICLR.
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Konferensbidrag (refereegranskat)abstract
- Unpaired image-to-image translation has attracted significant interest due to the invention of CycleGAN, a method which utilizes a combination of adversarial and cycle consistency losses to avoid the need for paired data. It is known that the CycleGAN problem might admit multiple solutions, and our goal in this paper is to analyze the space of exact solutions and to give perturbation bounds for approximate solutions. We show theoretically that the exact solution space is invariant with respect to automorphisms of the underlying probability spaces, and, furthermore, that the group of automorphisms acts freely and transitively on the space of exact solutions. We examine the case of zero 'pure' CycleGAN loss first in its generality, and, subsequently, expand our analysis to approximate solutions for 'extended' CycleGAN loss where identity loss term is included. In order to demonstrate that these results are applicable, we show that under mild conditions nontrivial smooth automorphisms exist. Furthermore, we provide empirical evidence that neural networks can learn these automorphisms with unexpected and unwanted results. We conclude that finding optimal solutions to the CycleGAN loss does not necessarily lead to the envisioned result in image-to-image translation tasks and that underlying hidden symmetries can render the result utterly useless.
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| 3. |
- Adler, Jonas, et al.
(författare)
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Banach Wasserstein GAN
- 2018
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Ingår i: Advances in Neural Information Processing Systems 31 (NIPS 2018). - : Neural Information Processing Systems (NIPS).
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Konferensbidrag (refereegranskat)abstract
- 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.
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| 4. |
- Adler, Jonas, 1990-
(författare)
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Data-driven Methods in Inverse Problems
- 2019
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- 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.
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| 5. |
- Adler, Jonas, et al.
(författare)
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Deep Bayesian Inversion
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- 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.
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| 6. |
- Adler, Jonas
(författare)
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Learned Iterative Reconstruction
- 2023
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Ingår i: Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging. - Cham : Springer Nature. ; , s. 751-771
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Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- Learned iterative reconstruction methods have recently emerged as a powerful tool to solve inverse problems. These deep learning techniques for image reconstruction achieve remarkable speed and accuracy by combining hard knowledge about the physics of the image formation process, represented by the forward operator, with soft knowledge about how the reconstructions should look like, represented by deep neural networks. A diverse set of such methods have been proposed, and this chapter seeks to give an overview of their similarities and differences, as well as discussing some of the commonly used methods to improve their performance.
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| 7. |
- Adler, Jonas, et al.
(författare)
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Learned Primal-Dual Reconstruction
- 2018
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Ingår i: IEEE Transactions on Medical Imaging. - : IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC. - 0278-0062 .- 1558-254X. ; 37:6, s. 1322-1332
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 8. |
- Adler, Jonas, et al.
(författare)
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Learning to solve inverse problems using Wasserstein loss
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- 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.
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| 9. |
- Adler, Jonas, et al.
(författare)
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Solving ill-posed inverse problems using iterative deep neural networks
- 2017
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Ingår i: Inverse Problems. - : Institute of Physics Publishing (IOPP). - 0266-5611 .- 1361-6420. ; 33:12
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Tidskriftsartikel (refereegranskat)abstract
- 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).
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| 10. |
- Adler, Jonas, et al.
(författare)
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Task adapted reconstruction for inverse problems
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- 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.
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