| 1. |
- 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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| 2. |
- 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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| 3. |
- 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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| 4. |
- 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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| 5. |
- 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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| 6. |
- Adler, Jonas, et al.
(författare)
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Task adapted reconstruction for inverse problems
- 2022
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Ingår i: Inverse Problems. - : IOP Publishing. - 0266-5611 .- 1361-6420. ; 38:7
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Tidskriftsartikel (refereegranskat)abstract
- The paper considers the problem of performing a post-processing 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 post-processing 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 post-processing 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 post-processing that can be encoded 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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| 7. |
- Andrade-Loarca, Hector, et al.
(författare)
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Deep microlocal reconstruction for limited-angle tomography
- 2022
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Ingår i: Applied and Computational Harmonic Analysis. - : Elsevier BV. - 1063-5203 .- 1096-603X. ; 59, s. 155-197
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Tidskriftsartikel (refereegranskat)abstract
- We present a deep-learning-based algorithm to jointly solve a reconstruction problem and a wavefront set extraction problem in tomographic imaging. The algorithm is based on a recently developed digital wavefront set extractor as well as the well-known microlocal canonical relation for the Radon transform. We use the wavefront set information about x-ray data to improve the reconstruction by requiring that the underlying neural networks simultaneously extract the correct ground truth wavefront set and ground truth image. As a necessary theoretical step, we identify the digital microlocal canonical relations for deep convolutional residual neural networks. We find strong numerical evidence for the effectiveness of this approach.
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| 8. |
- Andrade-Loarca, H., et al.
(författare)
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Extraction of digital wavefront sets using applied harmonic analysis and deep neural networks
- 2019
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Ingår i: SIAM Journal on Imaging Sciences. - : Society for Industrial & Applied Mathematics (SIAM). - 1936-4954. ; 12:4, s. 1936-1966
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Tidskriftsartikel (refereegranskat)abstract
- Microlocal analysis provides deep insight into singularity structures and is often crucial for solving inverse problems, predominately, in imaging sciences. Of particular importance is the analysis of wavefront sets and the correct extraction of those. In this paper, we introduce the first algorithmic approach to extract the wavefront set of images, which combines data-based and model-based methods. Based on a celebrated property of the shearlet transform to unravel information on the wavefront set, we extract the wavefront set of an image by first applying a discrete shearlet transform and then feeding local patches of this transform to a deep convolutional neural network trained on labeled data. The resulting algorithm outperforms all competing algorithms in edge-orientation and ramp-orientation detection.
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| 9. |
- Andrade-Loarca, Hector, et al.
(författare)
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Shearlets as feature extractor for semantic edge detection : the model-based and data-driven realm
- 2020
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Ingår i: Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences. - : The Royal Society. - 1364-5021 .- 1471-2946. ; 476:2243
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Tidskriftsartikel (refereegranskat)abstract
- Semantic edge detection has recently gained a lot of attention as an image-processing task, mainly because of its wide range of real-world applications. This is based on the fact that edges in images contain most of the semantic information. Semantic edge detection involves two tasks, namely pure edge detection and edge classification. Those are in fact fundamentally distinct in terms of the level of abstraction that each task requires. This fact is known as the distracted supervision paradox and limits the possible performance of a supervised model in semantic edge detection. In this work, we will present a novel hybrid method that is based on a combination of the model-based concept of shearlets, which provides probably optimally sparse approximations of a model class of images, and the data-driven method of a suitably designed convolutional neural network. We show that it avoids the distracted supervision paradox and achieves high performance in semantic edge detection. In addition, our approach requires significantly fewer parameters than a pure data-driven approach. Finally, we present several applications such as tomographic reconstruction and show that our approach significantly outperforms former methods, thereby also indicating the value of such hybrid methods for biomedical imaging.
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| 10. |
- Arridge, Simon, et al.
(författare)
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Solving inverse problems using data-driven models
- 2019
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Ingår i: Acta Numerica. - : Cambridge University Press. - 0962-4929 .- 1474-0508. ; 28, s. 1-174
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Tidskriftsartikel (refereegranskat)abstract
- Recent research in inverse problems seeks to develop a mathematically coherent foundation for combining data-driven models, and in particular those based on deep learning, with domain-specific knowledge contained in physical-analytical models. The focus is on solving ill-posed inverse problems that are at the core of many challenging applications in the natural sciences, medicine and life sciences, as well as in engineering and industrial applications. This survey paper aims to give an account of some of the main contributions in data-driven inverse problems.
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