| 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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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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| 5. |
- 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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| 6. |
- 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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| 7. |
- 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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| 8. |
- 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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| 9. |
- 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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| 10. |
- 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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| 11. |
- 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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| 12. |
- Aspri, A., et al.
(författare)
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A Data-Driven Iteratively Regularized Landweber Iteration
- 2020
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Ingår i: Numerical Functional Analysis and Optimization. - : Taylor and Francis Inc.. - 0163-0563 .- 1532-2467.
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Tidskriftsartikel (refereegranskat)abstract
- We derive and analyze a new variant of the iteratively regularized Landweber iteration, for solving linear and nonlinear ill-posed inverse problems. The method takes into account training data, which are used to estimate the interior of a black box, which is used to define the iteration process. We prove convergence and stability for the scheme in infinite dimensional Hilbert spaces. These theoretical results are complemented by some numerical experiments for solving linear inverse problems for the Radon transform and a nonlinear inverse problem for Schlieren tomography.
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| 13. |
- Banert, Sebastian, et al.
(författare)
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Accelerated Forward-Backward Optimization Using Deep Learning
- 2024
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Ingår i: SIAM Journal on Optimization. - : Society for Industrial & Applied Mathematics (SIAM). - 1052-6234 .- 1095-7189. ; 34:2, s. 1236-1263
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Tidskriftsartikel (refereegranskat)abstract
- We propose several deep -learning accelerated optimization solvers with convergence guarantees. We use ideas from the analysis of accelerated forward -backward schemes like FISTA, but instead of the classical approach of proving convergence for a choice of parameters, such as a step -size, we show convergence whenever the update is chosen in a specific set. Rather than picking a point in this set using some predefined method, we train a deep neural network to pick the best update within a given space. Finally, we show that the method is applicable to several cases of smooth and nonsmooth optimization and show superior results to established accelerated solvers.
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| 14. |
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| 15. |
- Banert, Sebastian, et al.
(författare)
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Data-driven nonsmooth optimization
- 2020
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Ingår i: SIAM Journal on Optimization. - : Society for Industrial & Applied Mathematics (SIAM). - 1052-6234 .- 1095-7189. ; 30:1, s. 102-131
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Tidskriftsartikel (refereegranskat)abstract
- In this work, we consider methods for solving large-scale optimization problems with a possibly nonsmooth objective function. The key idea is to first parametrize a class of optimization methods using a generic iterative scheme involving only linear operations and applications of proximal operators. This scheme contains some modern primal-dual first-order algorithms like the Douglas-Rachford and hybrid gradient methods as special cases. Moreover, we show weak convergence of the iterates to an optimal point for a new method which also belongs to this class. Next, we interpret the generic scheme as a neural network and use unsupervised training to learn the best set of parameters for a specific class of objective functions while imposing a fixed number of iterations. In contrast to other approaches of "learning to optimize," we present an approach which learns parameters only in the set of convergent schemes. Finally, we illustrate the approach on optimization problems arising in tomographic reconstruction and image deconvolution, and train optimization algorithms for optimal performance given a fixed number of iterations.
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| 16. |
- Bergstrand, Jan, et al.
(författare)
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Super-resolution microscopy can identify specific protein distribution patterns in platelets incubated with cancer cells
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- Protein contents in platelets are frequently changed upon tumor development and metastasis. However, how cancer cells can influence protein-selective redistribution and release within platelets, thereby promoting tumor development, remains largely elusive. With fluorescence-based super-resolution stimulated emission depletion (STED) imaging we reveal how specific proteins, implicated in tumor progression and metastasis, re-distribute within platelets, when subject to soluble activators (thrombin, adenosine-diphosphate and thromboxaneA2), and when incubated with cancer (MCF-7, MDA-MB-231, EFO21) or non-cancer cells (184A1, MCF10A). Upon cancer cell incubation, the cell-adhesion protein P-selectin was found to re-distribute into circular nano-structures, consistent with accumulation into the membrane of protein-storing alpha-granules within the platelets. These changes were to a significantly lesser extent, if at all, found in platelets incubated with normal cells, or in platelets subject to soluble platelet activators. From these patterns, we developed a classification procedure, whereby platelets exposed to cancer cells, to non-cancer cells, soluble activators as well as non-activated platelets all could be identified in an automatic, objective manner. We demonstrate that STED imaging, in contrast to electron and confocal microscopy, has the necessary spatial resolution and labelling efficiency to identify protein distribution patterns in platelets and can resolve how they specifically change upon different activations. Combined with image analyses of specific protein distribution patterns within the platelets, STED imaging can thus have a role in future platelet-based cancer diagnostics and therapeutic monitoring. The presented approach can also bring further clarity into fundamental mechanisms for cancer cell-platelet interactions, and into non-contact cell-to-cell interactions in general.
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| 17. |
- Bergstrand, Jan, et al.
(författare)
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Super-resolution microscopy can identify specific protein distribution patterns in platelets incubated with cancer cells
- 2019
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Ingår i: Nanoscale. - : ROYAL SOC CHEMISTRY. - 2040-3364 .- 2040-3372. ; 11:20, s. 10023-10033
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Tidskriftsartikel (refereegranskat)abstract
- Protein contents in platelets are frequently changed upon tumor development and metastasis. However, how cancer cells can influence protein-selective redistribution and release within platelets, thereby promoting tumor development, remains largely elusive. With fluorescence-based super-resolution stimulated emission depletion (STED) imaging we reveal how specific proteins, implicated in tumor progression and metastasis, re-distribute within platelets, when subject to soluble activators (thrombin, adenosine diphosphate and thromboxane A2), and when incubated with cancer (MCF-7, MDA-MB-231, EFO21) or non-cancer cells (184A1, MCF10A). Upon cancer cell incubation, the cell-adhesion protein P-selectin was found to re-distribute into circular nano-structures, consistent with accumulation into the membrane of protein-storing alpha-granules within the platelets. These changes were to a significantly lesser extent, if at all, found in platelets incubated with normal cells, or in platelets subject to soluble platelet activators. From these patterns, we developed a classification procedure, whereby platelets exposed to cancer cells, to non-cancer cells, soluble activators, as well as non-activated platelets all could be identified in an automatic, objective manner. We demonstrate that STED imaging, in contrast to electron and confocal microscopy, has the necessary spatial resolution and labelling efficiency to identify protein distribution patterns in platelets and can resolve how they specifically change upon different activations. Combined with image analyses of specific protein distribution patterns within the platelets, STED imaging can thus have a role in future platelet-based cancer diagnostics and therapeutic monitoring. The presented approach can also bring further clarity into fundamental mechanisms for cancer cell-platelet interactions, and into non-contact cell-to-cell interactions in general.
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| 18. |
- Buddenkotte, Thomas, et al.
(författare)
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Calibrating ensembles for scalable uncertainty quantification in deep learning-based medical image segmentation
- 2023
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Ingår i: Computers in Biology and Medicine. - : Elsevier Ltd. - 0010-4825 .- 1879-0534. ; 163
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Tidskriftsartikel (refereegranskat)abstract
- Uncertainty quantification in automated image analysis is highly desired in many applications. Typically, machine learning models in classification or segmentation are only developed to provide binary answers; however, quantifying the uncertainty of the models can play a critical role for example in active learning or machine human interaction. Uncertainty quantification is especially difficult when using deep learning-based models, which are the state-of-the-art in many imaging applications. The current uncertainty quantification approaches do not scale well in high-dimensional real-world problems. Scalable solutions often rely on classical techniques, such as dropout, during inference or training ensembles of identical models with different random seeds to obtain a posterior distribution. In this paper, we present the following contributions. First, we show that the classical approaches fail to approximate the classification probability. Second, we propose a scalable and intuitive framework for uncertainty quantification in medical image segmentation that yields measurements that approximate the classification probability. Third, we suggest the usage of k-fold cross-validation to overcome the need for held out calibration data. Lastly, we motivate the adoption of our method in active learning, creating pseudo-labels to learn from unlabeled images and human–machine collaboration.
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| 19. |
- Buddenkotte, Thomas, et al.
(författare)
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Deep learning-based segmentation of multisite disease in ovarian cancer
- 2023
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Ingår i: EUROPEAN RADIOLOGY EXPERIMENTAL. - : Springer Nature. - 2509-9280. ; 7:1
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Tidskriftsartikel (refereegranskat)abstract
- Purpose: To determine if pelvic/ovarian and omental lesions of ovarian cancer can be reliably segmented on computed tomography (CT) using fully automated deep learning-based methods.Methods: A deep learning model for the two most common disease sites of high-grade serous ovarian cancer lesions (pelvis/ovaries and omentum) was developed and compared against the well-established “no-new-Net” framework and unrevised trainee radiologist segmentations. A total of 451 CT scans collected from four different institutions were used for training (n = 276), evaluation (n = 104) and testing (n = 71) of the methods. The performance was evaluated using the Dice similarity coefficient (DSC) and compared using a Wilcoxon test.Results: Our model outperformed no-new-Net for the pelvic/ovarian lesions in cross-validation, on the evaluation and test set by a significant margin (p values being 4 × 10–7, 3 × 10–4, 4 × 10–2, respectively), and for the omental lesions on the evaluation set (p = 1 × 10–3). Our model did not perform significantly differently in segmenting pelvic/ovarian lesions (p = 0.371) compared to a trainee radiologist. On an independent test set, the model achieved a DSC performance of 71 ± 20 (mean ± standard deviation) for pelvic/ovarian and 61 ± 24 for omental lesions.Conclusion: Automated ovarian cancer segmentation on CT scans using deep neural networks is feasible and achieves performance close to a trainee-level radiologist for pelvic/ovarian lesions.Relevance statement: Automated segmentation of ovarian cancer may be used by clinicians for CT-based volumetric assessments and researchers for building complex analysis pipelines.Key points:The first automated approach for pelvic/ovarian and omental ovarian cancer lesion segmentation on CT images has been presented.Automated segmentation of ovarian cancer lesions can be comparable with manual segmentation of trainee radiologists.Careful hyperparameter tuning can provide models significantly outperforming strong state-of-the-art baselines. Graphical Abstract: [Figure not available: see fulltext.]
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| 20. |
- Chen, C., et al.
(författare)
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A new variational model for joint image reconstruction and motion estimation in spatiotemporal imaging
- 2019
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Ingår i: SIAM Journal on Imaging Sciences. - : Society for Industrial & Applied Mathematics (SIAM). - 1936-4954. ; 12:4, s. 1686-1719
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Tidskriftsartikel (refereegranskat)abstract
- We propose a new variational model for joint image reconstruction and motion estimation in spatiotemporal imaging, which is investigated along a general framework that we present with shape theory. This model consists of two components, one for conducting modified static image reconstruction, and the other performs sequentially indirect image registration. For the latter, we generalize the large deformation diffeomorphic metric mapping framework into the sequentially indirect registration setting. The proposed model is compared theoretically against alternative approaches (optical flow based model and diffeomorphic motion models), and we demonstrate that the proposed model has desirable properties in terms of the optimal solution. The theoretical derivations and efficient algorithms are also presented for a time-discretized scenario of the proposed model, which show that the optimal solution of the time-discretized version is consistent with that of the time-continuous one, and most of the computational components is the easy-implemented linearized deformation. The complexity of the algorithm is analyzed as well. This work is concluded by some numerical examples in 2D space + time tomography with very sparse and/or highly noisy data.
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| 21. |
- Chen, C., et al.
(författare)
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An efficient algorithm to compute the X-ray transform
- 2021
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Ingår i: International Journal of Computer Mathematics. - : Informa UK Limited. - 0020-7160 .- 1029-0265.
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Tidskriftsartikel (refereegranskat)abstract
- We propose a new algorithm to compute the X-ray transform of an image represented by unit (pixel/voxel) basis functions. The fundamental task is equivalently calculating the intersection lengths of the ray with associated units. For the given ray, we derive the sufficient and necessary condition for non-vanishing intersectability. By this condition, we can distinguish the units that produce valid intersections with the ray. Only for those units, we calculate the intersection lengths by the obtained analytic formula. The proposed algorithm is adapted to various two-dimensional (2D)/three-dimensional (3D) scanning geometries, and its several issues are also discussed, including the intrinsic ambiguity, flexibility, computational cost and parallelization. The proposed method is fast and easy to implement, more complete and flexible than the existing alternatives with respect to different scanning geometries and different basis functions. Finally, we validate the correctness of the algorithm.
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| 22. |
- Chen, C., et al.
(författare)
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Indirect image registration with large diffeomorphic deformations
- 2018
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Ingår i: SIAM Journal on Imaging Sciences. - : Society for Industrial and Applied Mathematics Publications. - 1936-4954. ; 11:1, s. 575-617
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Tidskriftsartikel (refereegranskat)abstract
- This paper adapts the large deformation diffeomorphic metric mapping framework for image registration to the indirect setting, where a template is registered against a target that is given through indirect noisy observations. The registration uses diffeomorphisms that transform the template through a (group) action. These diffeomorphisms are generated by solving a flow equation that is defined by a velocity field with certain regularity. The theoretical analysis includes a proof that indirect image registration has solutions (existence) that are stable and that converge as the data error tends to zero, so it becomes a well-defined regularization method. The paper concludes with examples of indirect image registration in 2D tomography with very sparse and/or highly noisy data.
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| 23. |
- Diepeveen, Willem, et al.
(författare)
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Regularizing Orientation Estimation in Cryogenic Electron Microscopy Three-Dimensional Map Refinement through Measure-Based Lifting over Riemannian Manifolds
- 2023
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Ingår i: SIAM Journal on Imaging Sciences. - : Society for Industrial & Applied Mathematics (SIAM). - 1936-4954. ; 16:3, s. 1440-1490
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Tidskriftsartikel (refereegranskat)abstract
- Motivated by the trade-off between noise robustness and data consistency for joint three-imensional (3D) map reconstruction and rotation estimation in single particle cryogenic-electron microscopy (Cryo-EM), we propose ellipsoidal support lifting (ESL), a measure-based lifting scheme for regularizing and approximating the global minimizer of a smooth function over a Riemannian manifold. Under a uniqueness assumption on the minimizer we show several theoretical results, in particular well-posedness of the method and an error bound due to the induced bias with respect to the global minimizer. Additionally, we use the developed theory to integrate the measure-based lifting scheme into an alternating update method for joint homogeneous 3D map reconstruction and rotation estimation, where typically tens of thousands of manifold-valued minimization problems have to be solved and where regularization is necessary because of the high noise levels in the data. The joint recovery method is used to test both the theoretical predictions and algorithmic performance through numerical experiments with Cryo-EM data. In particular, the induced bias due to the regularizing effect of ESL empirically estimates better rotations, i.e., rotations closer to the ground truth, than global optimization would.
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| 24. |
- Dong, G., et al.
(författare)
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Infinite dimensional optimization models and PDEs for dejittering
- 2015
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Ingår i: 5th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2015. - Cham : Elsevier. - 9783319184609 ; , s. 678-689
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Konferensbidrag (refereegranskat)abstract
- In this paper we do a systematic investigation of continuous methods for pixel, line pixel and line dejittering. The basis for these investigations are the discrete line dejittering algorithm of Nikolova and the partial differential equation of Lenzen et al for pixel dejittering. To put these two different worlds in perspective we find infinite dimensional optimization algorithms linking to the finite dimensional optimization problems and formal flows associated with the infinite dimensional optimization problems. Two different kinds of optimization problems will be considered: Dejittering algorithms for determining the displacement and displacement error correction formulations, which correct the jittered image, without estimating the jitter. As a by-product we find novel variational methods for displacement error regularization and unify them into one family. The second novelty is a comprehensive comparison of the different models for different types of jitter, in terms of efficiency of reconstruction and numerical complexity.
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| 25. |
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| 26. |
- Eguizabal, Alma, et al.
(författare)
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Learned Material Decomposition for Photon Counting CT
- 2021
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Ingår i: Proceedings of the 16th Virtual International Meeting onFully 3D Image Reconstruction inRadiology and Nuclear Medicine. ; , s. 15-19
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)
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| 27. |
- Esteve-Yague, Carlos, et al.
(författare)
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Spectral decomposition of atomic structures in heterogeneous cryo-EM
- 2023
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Ingår i: Inverse Problems. - : IOP Publishing. - 0266-5611 .- 1361-6420. ; 39:3, s. 034003-
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Tidskriftsartikel (refereegranskat)abstract
- We consider the problem of recovering the three-dimensional atomic structure of a flexible macromolecule from a heterogeneous cryogenic electron microscopy (cryo-EM) dataset. The dataset contains noisy tomographic projections of the electrostatic potential of the macromolecule, taken from different viewing directions, and in the heterogeneous case, each cryo-EM image corresponds to a different conformation of the macromolecule. Under the assumption that the macromolecule can be modelled as a chain, or discrete curve (as it is for instance the case for a protein backbone with a single chain of amino-acids), we introduce a method to estimate the deformation of the atomic model with respect to a given conformation, which is assumed to be known a priori. Our method consists on estimating the torsion and bond angles of the atomic model in each conformation as a linear combination of the eigenfunctions of the Laplace operator in the manifold of conformations. These eigenfunctions can be approximated by means of a well-known technique in manifold learning, based on the construction of a graph Laplacian using the cryo-EM dataset. Finally, we test our approach with synthetic datasets, for which we recover the atomic model of two-dimensional and three-dimensional flexible structures from simulated cryo-EM images.
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| 28. |
- Gopinath, A., et al.
(författare)
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Shape-based regularization of electron tomographic reconstruction
- 2012
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Ingår i: IEEE Transactions on Medical Imaging. - 0278-0062 .- 1558-254X. ; 31:12, s. 2241-2252
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Tidskriftsartikel (refereegranskat)abstract
- We introduce a tomographic reconstruction method implemented using a shape-based regularization technique. Spatial models of known features in the structure being reconstructed are integrated into the reconstruction process as regularizers. Our regularization scheme is driven locally through shape information obtained from segmentation and compared with a known spatial model. We demonstrated our method on tomography data from digital phantoms, simulated data, and experimental electron tomography (ET) data of virus complexes. Our reconstruction showed reduced blurring and an improvement in the resolution of the reconstructed volume was also measured. This method also produced improved demarcation of spike boundaries in viral membranes when compared with popular techniques like weighted back projection and the algebraic reconstruction technique. Improved ET reconstructions will provide better structure elucidation and improved feature visualization, which can aid in solving key biological issues. Our method can also be generalized to other tomographic modalities.
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| 29. |
- Gris, Barbara, et al.
(författare)
-
Image reconstruction through metamorphosis
- 2020
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Ingår i: Inverse Problems. - : IOP PUBLISHING LTD. - 0266-5611 .- 1361-6420. ; 36:2
-
Tidskriftsartikel (refereegranskat)abstract
- The paper describes a method for reconstructing an image from noisy and indirect observations by registering, via metamorphosis, a template. The image registration part consists of two components, one is a geometric deformation that moves intensities without changing them and the other that changes intensity values. Unlike a registration with only geometrical deformation, this framework gives good results also when intensities of the template are poorly chosen. It also allows for appearance of a new structure. The approach is applicable to general inverse problems in imaging and we prove existence, stability and convergence, which implies that the method is a well-defined regularisation method. We also present several numerical examples from tomography.
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| 30. |
- Hahn, S., et al.
(författare)
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Spectral transfer from phase to intensity in Fresnel diffraction
- 2016
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Ingår i: PHYSICAL REVIEW A. - : American Physical Society. - 2469-9926. ; 93:5
-
Tidskriftsartikel (refereegranskat)abstract
- We analyze theoretically and investigate experimentally the transfer of phase to intensity power spectra of spatial frequencies through free-space Fresnel diffraction. Depending on lambda z (where lambda is the wavelength and z is the free-space propagation distance) and the phase-modulation strength S, we demonstrate that for multiscale and broad phase spectra critical behavior transmutes a quasilinear to a nonlinear diffractogram except for low frequencies. On the contrary, a single-scale and broad phase spectrum induces a critical transition in the diffractogram at low frequencies. In both cases, identifying critical behavior encoded in the intensity power spectra is of fundamental interest because it exhibits the limits of perturbative power counting but also guides resolution and contrast optimization in propagation-based, single-distance, phase-contrast imaging, given certain dose and coherence constraints.
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| 31. |
- Hauptmann, Andreas, et al.
(författare)
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Multi-Scale Learned Iterative Reconstruction
- 2020
-
Ingår i: IEEE Transactions on Computational Imaging. - : Institute of Electrical and Electronics Engineers (IEEE). - 2573-0436 .- 2333-9403. ; 6, s. 843-856
-
Tidskriftsartikel (refereegranskat)abstract
- Model-based learned iterative reconstruction methods have recently been shown to outperform classical reconstruction algorithms. Applicability of these methods to large scale inverse problems is however limited by the available memory for training and extensive training times, the latter due to computationally expensive forward models. As a possible solution to these restrictions we propose a multi-scale learned iterative reconstruction scheme that computes iterates on discretisations of increasing resolution. This procedure does not only reduce memory requirements, it also considerably speeds up reconstruction and training times, but most importantly is scalable to large scale inverse problems with non-trivial forward operators, such as those that arise in many 3D tomographic applications. In particular, we propose a hybrid network that combines the multi-scale iterative approach with a particularly expressive network architecture which in combination exhibits excellent scalability in 3D. Applicability of the algorithm is demonstrated for 3D cone beam computed tomography from real measurement data of an organic phantom. Additionally, we examine scalability and reconstruction quality in comparison to established learned reconstruction methods in two dimensions for low dose computed tomography on human phantoms.
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| 32. |
- Kimanius, Dari, et al.
(författare)
-
Exploiting prior knowledge about biological macromolecules in cryo-EM structure determination
- 2024
-
Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- Three-dimensional reconstruction of the electron scattering potential of biological macromolecules from electron cryo-microscopy (cryo-EM) projection images is an ill-posed problem. The most popular cryo-EM software solutions to date rely on a regularisation approach that is based on the prior assumption that the scattering potential varies smoothly over three-dimensional space. Although this approach has been hugely successful in recent years, the amount of prior knowledge it exploits compares unfavourably to the knowledge about biological structures that has been accumulated over decades of research in structural biology. Here, we present a regularisation framework for cryo-EM structure determination that exploits prior knowledge about biological structures through a convolutional neural network that is trained on known macromolecular structures. We insert this neural network into the iterative cryo-EM structure determination process through an approach that is inspired by Regularisation by Denoising. We show that the new regularisation approach yields better reconstructions than the current state-of-the-art for simulated data and discuss options to extend this work for application to experimental cryo-EM data.
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| 33. |
- Kimanius, Dari, et al.
(författare)
-
Exploiting prior knowledge about biological macromolecules in cryo-EM structure determination
- 2021
-
Ingår i: IUCrJ. - : International Union of Crystallography (IUCr). - 2052-2525. ; 8, s. 60-75
-
Tidskriftsartikel (refereegranskat)abstract
- Three-dimensional reconstruction of the electron-scattering potential of biological macromolecules from electron cryo-microscopy (cryo-EM) projection images is an ill-posed problem. The most popular cryo-EM software solutions to date rely on a regularization approach that is based on the prior assumption that the scattering potential varies smoothly over three-dimensional space. Although this approach has been hugely successful in recent years, the amount of prior knowledge that it exploits compares unfavorably with the knowledge about biological structures that has been accumulated over decades of research in structural biology. Here, a regularization framework for cryo-EM structure determination is presented that exploits prior knowledge about biological structures through a convolutional neural network that is trained on known macromolecular structures. This neural network is inserted into the iterative cryo-EM structure-determination process through an approach that is inspired by regularization by denoising. It is shown that the new regularization approach yields better reconstructions than the current state of the art for simulated data, and options to extend this work for application to experimental cryo-EM data are discussed.
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| 34. |
- Lang, L. F., et al.
(författare)
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Template-Based Image Reconstruction from Sparse Tomographic Data
- 2019
-
Ingår i: Applied mathematics and optimization. - : Springer New York LLC. - 0095-4616 .- 1432-0606.
-
Tidskriftsartikel (refereegranskat)abstract
- We propose a variational regularisation approach for the problem of template-based image reconstruction from indirect, noisy measurements as given, for instance, in X-ray computed tomography. An image is reconstructed from such measurements by deforming a given template image. The image registration is directly incorporated into the variational regularisation approach in the form of a partial differential equation that models the registration as either mass- or intensity-preserving transport from the template to the unknown reconstruction. We provide theoretical results for the proposed variational regularisation for both cases. In particular, we prove existence of a minimiser, stability with respect to the data, and convergence for vanishing noise when either of the abovementioned equations is imposed and more general distance functions are used. Numerically, we solve the problem by extending existing Lagrangian methods and propose a multilevel approach that is applicable whenever a suitable downsampling procedure for the operator and the measured data can be provided. Finally, we demonstrate the performance of our method for template-based image reconstruction from highly undersampled and noisy Radon transform data. We compare results for mass- and intensity-preserving image registration, various regularisation functionals, and different distance functions. Our results show that very reasonable reconstructions can be obtained when only few measurements are available and demonstrate that the use of a normalised cross correlation-based distance is advantageous when the image intensities between the template and the unknown image differ substantially.
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| 35. |
- Lunz, S., et al.
(författare)
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Adversarial regularizers in inverse problems
- 2018
-
Ingår i: Advances in Neural Information Processing Systems. - : Neural information processing systems foundation. ; , s. 8507-8516
-
Konferensbidrag (refereegranskat)abstract
- Inverse Problems in medical imaging and computer vision are traditionally solved using purely model-based methods. Among those variational regularization models are one of the most popular approaches. We propose a new framework for applying data-driven approaches to inverse problems, using a neural network as a regularization functional. The network learns to discriminate between the distribution of ground truth images and the distribution of unregularized reconstructions. Once trained, the network is applied to the inverse problem by solving the corresponding variational problem. Unlike other data-based approaches for inverse problems, the algorithm can be applied even if only unsupervised training data is available. Experiments demonstrate the potential of the framework for denoising on the BSDS dataset and for computed tomography reconstruction on the LIDC dataset.
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| 36. |
- Mukherjee, S., et al.
(författare)
-
Adversarially Learned Iterative Reconstruction for Imaging Inverse Problems
- 2021
-
Ingår i: 8th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2021. - Cham : Springer Science and Business Media Deutschland GmbH. ; , s. 540-552
-
Konferensbidrag (refereegranskat)abstract
- In numerous practical applications, especially in medical image reconstruction, it is often infeasible to obtain a large ensemble of ground-truth/measurement pairs for supervised learning. Therefore, it is imperative to develop unsupervised learning protocols that are competitive with supervised approaches in performance. Motivated by the maximum-likelihood principle, we propose an unsupervised learning framework for solving ill-posed inverse problems. Instead of seeking pixel-wise proximity between the reconstructed and the ground-truth images, the proposed approach learns an iterative reconstruction network whose output matches the ground-truth in distribution. Considering tomographic reconstruction as an application, we demonstrate that the proposed unsupervised approach not only performs on par with its supervised variant in terms of objective quality measures, but also successfully circumvents the issue of over-smoothing that supervised approaches tend to suffer from. The improvement in reconstruction quality comes at the expense of higher training complexity, but, once trained, the reconstruction time remains the same as its supervised counterpart.
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| 37. |
- Mukherjee, S., et al.
(författare)
-
DATA-DRIVEN CONVEX REGULARIZERS FOR INVERSE PROBLEMS
- 2024
-
Ingår i: 2024 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2024 - Proceedings. - : Institute of Electrical and Electronics Engineers (IEEE). ; , s. 13386-13390
-
Konferensbidrag (refereegranskat)abstract
- We propose to learn a data-adaptive convex regularizer, which is parameterized using an input-convex neural network (ICNN), for variational image reconstruction. The regularizer parameters are learned adversarially by telling apart clean images from the artifact-ridden ones in a training dataset. Convexity of the regularizer is theoretically and practically important since (i) one can establish well-posedness guarantees for the corresponding variational reconstruction problem and (ii) devise provably convergent optimization algorithms for reconstruction. In particular, the resulting method is shown to be convergent in the sense of regularization and can be solved provably using a gradient-based solver. To demonstrate the performance of our approach for solving inverse problems, we consider deblurring natural images and reconstruction in X-ray computed tomography (CT) and show that the proposed convex regularizer is on par with and sometimes superior to state-of-the-art classical and data-driven techniques for inverse problems, especially with severely ill-posed forward operators (such as in limited-angle tomography).
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| 38. |
- Mukherjee, Subhadip, et al.
(författare)
-
End-to-end reconstruction meets data-driven regularization for inverse problems
- 2021
-
Ingår i: Advances in Neural Information Processing Systems. - : Neural information processing systems foundation. ; , s. 21413-21425
-
Konferensbidrag (refereegranskat)abstract
- We propose a new approach for learning end-to-end reconstruction operators based on unpaired training data for ill-posed inverse problems. The proposed method combines the classical variational framework with iterative unrolling and essentially seeks to minimize a weighted combination of the expected distortion in the measurement space and the Wasserstein-1 distance between the distributions of the reconstruction and the ground-truth. More specifically, the regularizer in the variational setting is parametrized by a deep neural network and learned simultaneously with the unrolled reconstruction operator. The variational problem is then initialized with the output of the reconstruction network and solved iteratively till convergence. Notably, it takes significantly fewer iterations to converge as compared to variational methods, thanks to the excellent initialization obtained via the unrolled operator. The resulting approach combines the computational efficiency of end-to-end unrolled reconstruction with the well-posedness and noise-stability guarantees of the variational setting. Moreover, we demonstrate with the example of image reconstruction in X-ray computed tomography (CT) that our approach outperforms state-of-the-art unsupervised methods and that it outperforms or is at least on par with state-of-the-art supervised data-driven reconstruction approaches.
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| 39. |
- Mukherjee, Subhadip, et al.
(författare)
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Learned Reconstruction Methods With Convergence Guarantees : A survey of concepts and applications
- 2023
-
Ingår i: IEEE signal processing magazine (Print). - : Institute of Electrical and Electronics Engineers (IEEE). - 1053-5888 .- 1558-0792. ; 40:1, s. 164-182
-
Tidskriftsartikel (refereegranskat)abstract
- In recent years, deep learning has achieved remarkable empirical success for image reconstruction. This has catalyzed an ongoing quest for the precise characterization of the correctness and reliability of data-driven methods in critical use cases, for instance, in medical imaging. Notwithstanding the excellent performance and efficacy of deep learning-based methods, concerns have been raised regarding the approaches' stability, or lack thereof, with serious practical implications. Significant advances have been made in recent years to unravel the inner workings of data-driven image recovery methods, challenging their widely perceived black-box nature. In this article, we specify relevant notions of convergence for data-driven image reconstruction, which forms the basis of a survey of learned methods with mathematically rigorous reconstruction guarantees. An example that is highlighted is the role of input-convex neural networks (ICNNs), offering the possibility to combine the power of deep learning with classical convex regularization theory for devising methods that are provably convergent. This survey article is aimed at both methodological researchers seeking to advance the frontiers of our understanding of data-driven image reconstruction methods as well as practitioners by providing an accessible description of useful convergence concepts and by placing some of the existing empirical practices on a solid mathematical foundation.
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| 40. |
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| 41. |
- Norlén, L., et al.
(författare)
-
Molecular cryo-electron tomography of vitreous tissue sections : current challenges
- 2009
-
Ingår i: Journal of Microscopy. - : Wiley. - 0022-2720 .- 1365-2818. ; 235:3, s. 293-307
-
Tidskriftsartikel (refereegranskat)abstract
- Electron tomography of vitreous tissue sections (tissue TOVIS) allows the study of the three-dimensional structure of molecular complexes in a near-native cellular context. Its usage is, however, limited by an unfortunate combination of noisy and incomplete data, by a technically demanding sample preparation procedure, and by a disposition for specimen degradation during data collection. Here we outline some major challenges as experienced from the application of TOVIS to human skin. We further consider a number of practical measures as well as theoretical approaches for its future development.
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| 42. |
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| 43. |
- Reuss, Matthias, et al.
(författare)
-
Measuring true localization accuracy in super resolution microscopy with DNA-origami nanostructures
- 2017
-
Ingår i: New Journal of Physics. - : Institute of Physics Publishing (IOPP). - 1367-2630. ; 19:2
-
Tidskriftsartikel (refereegranskat)abstract
- A common method to assess the performance of (super resolution) microscopes is to use the localization precision of emitters as an estimate for the achieved resolution. Naturally, this is widely used in super resolution methods based on single molecule stochastic switching. This concept suffers from the fact that it is hard to calibrate measures against a real sample (a phantom), because true absolute positions of emitters are almost always unknown. For this reason, resolution estimates are potentially biased in an image since one is blind to true position accuracy, i.e. deviation in position measurement from true positions. We have solved this issue by imaging nanorods fabricated with DNA-origami. The nanorods used are designed to have emitters attached at each end in a well-defined and highly conserved distance. These structures are widely used to gauge localization precision. Here, we additionally determined the true achievable localization accuracy and compared this figure of merit to localization precision values for two common super resolution microscope methods STED and STORM.
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| 44. |
- Ringh, Axel, et al.
(författare)
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High-level algorithm prototyping : An example extending the TVR-DART algorithm
- 2017
-
Ingår i: Discrete Geometry for Computer Imagery. - Cham : Springer. - 9783319662718 ; , s. 109-121
-
Bokkapitel (refereegranskat)abstract
- Operator Discretization Library (ODL) is an open-source Python library for prototyping reconstruction methods for inverse problems, and ASTRA is a high-performance Matlab/Python toolbox for large-scale tomographic reconstruction. The paper demonstrates the feasibility of combining ODL with ASTRA to prototype complex reconstruction methods for discrete tomography. As a case in point, we consider the total-variation regularized discrete algebraic reconstruction technique (TVR-DART). TVR-DART assumes that the object to be imaged consists of a limited number of distinct materials. The ODL/ASTRA implementation of this algorithm makes use of standardized building blocks, that can be combined in a plug-and-play manner. Thus, this implementation of TVR-DART can easily be adapted to account for application specific aspects, such as various noise statistics that come with different imaging modalities.
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| 45. |
- Rudzusika, Jevgenija, et al.
(författare)
-
Deep Learning-Based Dictionary Learning and Tomographic Image Reconstruction
- 2022
-
Ingår i: SIAM Journal on Imaging Sciences. - : Society for Industrial & Applied Mathematics (SIAM). - 1936-4954. ; 15:4, s. 1729-1764
-
Tidskriftsartikel (refereegranskat)abstract
- This work presents an approach for image reconstruction in clinical low-dose tomography that combines principles from sparse signal processing with ideas from deep learning. First, we describe sparse signal representation in terms of dictionaries from a statistical perspective and interpret dictionary learning as a process of aligning the distribution that arises from a generative model with the empirical distribution of true signals. As a result, we can see that sparse coding with learned dictionaries resembles a specific variational autoencoder, where the encoder is a sparse coding algorithm and the decoder is a linear function. Next, we show that dictionary learning can also benefit from computational advancements introduced in the context of deep learning, such as parallelism and stochastic optimization. Finally, we show that regularization by dictionaries achieves competitive performance in computed tomography reconstruction compared to state-of-the-art model-based and data-driven approaches, while being unsupervised with respect to tomographic data.
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| 46. |
- Rullgard, H., et al.
(författare)
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Simulation of transmission electron microscope images of biological specimens
- 2011
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Ingår i: Journal of Microscopy. - : Wiley. - 0022-2720 .- 1365-2818. ; 243:3, s. 234-256
-
Tidskriftsartikel (refereegranskat)abstract
- We present a new approach to simulate electron cryo-microscope images of biological specimens. The framework for simulation consists of two parts; the first is a phantom generator that generates a model of a specimen suitable for simulation, the second is a transmission electron microscope simulator. The phantom generator calculates the scattering potential of an atomic structure in aqueous buffer and allows the user to define the distribution of molecules in the simulated image. The simulator includes a well defined electron-specimen interaction model based on the scalar Schrodinger equation, the contrast transfer function for optics, and a noise model that includes shot noise as well as detector noise including detector blurring. To enable optimal performance, the simulation framework also includes a calibration protocol for setting simulation parameters. To test the accuracy of the new framework for simulation, we compare simulated images to experimental images recorded of the Tobacco Mosaic Virus (TMV) in vitreous ice. The simulated and experimental images show good agreement with respect to contrast variations depending on dose and defocus. Furthermore, random fluctuations present in experimental and simulated images exhibit similar statistical properties. The simulator has been designed to provide a platform for development of new instrumentation and image processing procedures in single particle electron microscopy, two-dimensional crystallography and electron tomography with well documented protocols and an open source code into which new improvements and extensions are easily incorporated.
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| 47. |
- Sanchez, Lorena Escudero, et al.
(författare)
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Integrating Artificial Intelligence Tools in the Clinical Research Setting : The Ovarian Cancer Use Case
- 2023
-
Ingår i: Diagnostics. - : MDPI. - 2075-4418. ; 13:17
-
Tidskriftsartikel (refereegranskat)abstract
- Artificial intelligence (AI) methods applied to healthcare problems have shown enormous potential to alleviate the burden of health services worldwide and to improve the accuracy and reproducibility of predictions. In particular, developments in computer vision are creating a paradigm shift in the analysis of radiological images, where AI tools are already capable of automatically detecting and precisely delineating tumours. However, such tools are generally developed in technical departments that continue to be siloed from where the real benefit would be achieved with their usage. Significant effort still needs to be made to make these advancements available, first in academic clinical research and ultimately in the clinical setting. In this paper, we demonstrate a prototype pipeline based entirely on open-source software and free of cost to bridge this gap, simplifying the integration of tools and models developed within the AI community into the clinical research setting, ensuring an accessible platform with visualisation applications that allow end-users such as radiologists to view and interact with the outcome of these AI tools.
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| 48. |
- Siadat, Medya, et al.
(författare)
-
Joint Image Deconvolution and Separation Using Mixed Dictionaries
- 2019
-
Ingår i: IEEE Transactions on Image Processing. - : Institute of Electrical and Electronics Engineers (IEEE). - 1057-7149 .- 1941-0042. ; 28:8, s. 3936-3945
-
Tidskriftsartikel (refereegranskat)abstract
- The task of separating an image into distinct components that represent different features plays an important role in many applications. Traditionally, such separation techniques are applied once the image in question has been reconstructed from measured data. We propose an efficient iterative algorithm, where reconstruction is performed jointly with the task of separation. A key assumption is that the image components have different sparse representations. The algorithm is based on a scheme that minimizes a functional composed of a data discrepancy term and the l(1)-norm of the coefficients of the different components with respect to their corresponding dictionaries. The performance is demonstrated for joint 2D deconvolution and separation into curve- and point-like components, and tests are performed on synthetic data as well as experimental stimulated emission depletion and confocal microscopy data. Experiments show that such a joint approach outperforms a sequential approach, where one first deconvolves data and then applies image separation.
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| 49. |
- Siadat, Medya, et al.
(författare)
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Reordering for improving global Arnoldi-Tikhonov method in image restoration problems
- 2018
-
Ingår i: Signal, Image and Video Processing. - : Springer London. - 1863-1703 .- 1863-1711. ; 12:3, s. 497-504
-
Tidskriftsartikel (refereegranskat)abstract
- This paper discusses the solution of large-scale linear discrete ill-posed problems arising from image restoration problems. Since the scale of the problem is usually very large, the computations with the blurring matrix can be very expensive. In this regard, we consider problems in which the coefficient matrix is the sum of Kronecker products of matrices to benefit the computation. Here, we present an alternative approach based on reordering of the image approximations obtained with the global Arnoldi-Tikhonov method. The ordering of the intensities is such that it makes the image approximation monotonic and thus minimizes the finite differences norm. We present theoretical properties of the method and numerical experiments on image restoration.
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| 50. |
- Ström, Emanuel, et al.
(författare)
-
Photon-Counting CT Reconstruction With a Learned Forward Operator
- 2022
-
Ingår i: IEEE Transactions on Computational Imaging. - : Institute of Electrical and Electronics Engineers (IEEE). - 2573-0436 .- 2333-9403. ; 8, s. 536-550
-
Tidskriftsartikel (refereegranskat)abstract
- Photon-Counting CT is an emerging imaging technology that promises higher spatial resolution and the possibility for material decomposition in the reconstruction. A major difficulty in Photon-Counting CT is to efficiently model cross-talk between detectors. In this work, we accelerate image reconstruction tasks for Photon-Counting CT by modelling the cross-talk with an appropriately trained deep convolutional neural network. The main result relates to proving convergence when using such a learned cross-talk model in the context of second-order optimisation methods for spectral CT. Another is to evaluate the method through numerical experiments on small-scale CT acquisitions generated using a realistic physics model. Using the reconstruction with a full cross-talk model as ground truth, the learned cross-talk model results in a 20 dB increase in peak-signal-to noise ratio compared to ignoring crass-talk altogether. At the same time, it effectively cuts the computation time of the full cross-talk model in half. Furthermore, the learned cross-talk model generalises well to both unseen data and unseen detector settings. Our results indicate that such a partially learned forward operator is a suitable way of modelling data generation in Photon-Counting CT with a computational benefit that becomes more noticeable for realistic problem sizes.
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