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Unrolled Neural Networks (NNs) have been extensively applied to different image reconstruction problems across all imaging modalities. A key component of the latter is that they allow for physics-informed learning of the regularization method which is parametrized by the NN. However, due to the lack of understanding of deep NNs from a theoretical point of view, unrolled NNs are still black-boxes when the regularizers are given by deep NNs, e.g. U-Nets.Dictionary Learning (DL) is a well-established regularization method which is based on learning a transform to sparsely approximate the signals of interest. Typically, DL-based image reconstruction either employs a dictionary which was pre-trained on a set of patches which were extracted from ground-truth images or a dictionary which is jointly trained during the reconstruction. However, in both cases, the used DL-algorithms are not designed to take into account the reconstruction problem or the underlying physical model which describes the imaging process. In this work, we propose a DL-algorithm based on unrolled NNs to overcome these limitations.We construct an unrolled NN which corresponds to an unrolled DL-based reconstruction algorithm and train the unrolled NN to optimize its weights, i.e. the atoms of the dictionary, by back-propagation in a supervised manner. Further, we propose a new way to employ a 2D dictionary in the spatio-temporal domain. We tested and evaluated the method on an accelerated cardiac cine MR image reconstruction problem using 216/36/36 dynamic images for training, validation and testing and compared it to two well-known state-of-the-art approaches for cardiac cine MRI based on deep iterative CNNs. Further, we analyze the obtained dictionaries in terms of dictionary-coherence and structure of the atoms. Last, we compare the reported methods in terms of stability by applying them to an entirely different dataset consisting of 49 different test images.The investigated physics-informed DL-approach yields significantly more accurate reconstructions compared to the DL-method which uses dictionaries obtained by decoupled pre-training, thereby providing an improvement of up to 4.90 dB in terms of PSNR and 5% in terms of SSIM. Further, the proposed spatio-temporal 2D dictionary outperforms the 1D and 3D dictionaries by preventing smoothing of image details while still accurately removing undersampling artefacts and noise resulting in an increase of up to 1.10 dB in terms of PSNR and 4% in terms of SSIM. Although being surpassed by the CNNs on the first dataset, the proposed NNs-based DL-method is more stable compared to the latter approach and yields comparable results on the second dataset. Last, it has the advantage of being entirely interpretable in each component.The presented physics-informed NN can be used as training algorithm for a classical and interpretable data-driven regularization method based a learned dictionary which can then not only be linked to the considered data but also to the reconstruction method that the NN defines. This article is protected by copyright. All rights reserved.

Objective. To provide 3D high-resolution cardiac T1 maps using model-based super-resolution reconstruction (SRR). Approach. Due to signal-to-noise ratio limitations and the motion of the heart during imaging, often 2D T1 maps with only low through-plane resolution (i.e. slice thickness of 6–8 mm) can be obtained. Here, a model-based SRR approach is presented, which combines multiple stacks of 2D acquisitions with 6–8 mm slice thickness and generates 3D high-resolution T1 maps with a slice thickness of 1.5–2 mm. Every stack was acquired in a different breath hold (BH) and any misalignment between BH was corrected retrospectively. The novelty of the proposed approach is the BH correction and the application of model-based SRR on cardiac T1 Mapping. The proposed approach was evaluated in numerical simulations and phantom experiments and demonstrated in four healthy subjects. Main results. Alignment of BH states was essential for SRR even in healthy volunteers. In simulations, respiratory motion could be estimated with an RMS error of 0.18 ± 0.28 mm. SRR improved the visualization of small structures. High accuracy and precision (average standard deviation of 69.62 ms) of the T1 values was ensured by SRR while the detectability of small structures increased by 40%. Significance. The proposed SRR approach provided T1 maps with high in-plane and high through-plane resolution (1.3 × 1.3 × 1.5–2 mm3). The approach led to improvements in the visualization of small structures and precise T1 values.

Thermal imaging for unmanned aerial vehicles is used to search for victims in poor visibility conditions. We used a gimbal-mounted camera for thermo-radiation measurements of body temperature from persons covered with rescue blankets in the hibernal wilderness setting. Long-wave infrared radiation in the spectral range between 7500 and 13,500 nm was evaluated. Parts of this research have previously been published in a review on electromagnetic radiation reflectivity of rescue blankets (https://www.mdpi.com/2079-6412/10/4/375/htm). Surface temperature measurement was diminished by clothing, namely by 72.6% for fleece, by 82.2% for an additional down jacket and by 92.3% for an additional all-weather jacket, as compared to forehead temperature. Furthermore, we detected that a single-layer rescue blanket is sufficient to render recognition of a body shape impossible. With three layers covering a clothed body infrared transmission was almost completely blocked. However, rescue blankets increase visibility for thermal cameras due to high gradients in temperature. Conspicuously low temperatures from objects of 1 to 2 m length may indicate reflections from rescue blanket surfaces in a cold environment. Ideally, rescue blankets should be removed from the body to increase the chance of being located when using thermal imaging to search for victims in search and rescue missions.

Worldwide, mountain forests represent a significant factor in reducing rockfall risk over long periods of time on large potential disposition areas. While the economic value of technical protection measures against rockfall can be clearly determined and their benefits indicated, there is no general consensus on the quantification of the protective effect of forests. Experience shows that wherever there is forest, the implementation of technical measures to reduce risk of rockfall might often be dispensable or cheaper, and large deforestations (e.g. after windthrows, forest fires, clear-cuts) often show an increased incidence of rockfall events. This study focussed on how the protective effect of a forest against rockfall can be quantified on an alpine transregional scale. We therefore estimated the runout length, in terms of the angle of reach, of 700 individual rockfall trajectories from 39 release areas from Austria, Germany, Italy and Slovenia. All recorded rockfall events passed through forests which were classified either as coppice forests or, according to the CORINE classification of land cover, as mixed, coniferous or broadleaved dominated high forest stands. For each individual rockfall trajectory, we measured the forest structural parameters stem number, basal area, top height, ratio of shrub to high forest and share of coniferous trees. To quantify the protective effect of forests on rockfall, a hazard reduction factor is introduced, defined as the ratio between an expected angle of reach without forest and the back-calculated forest-influenced angles of reach. The results show that forests significantly reduce the runout length of rockfall. The highest reduction was observed for mixed high forest stands, while the lowest hazard reduction was observed for high forest stands dominated either by coniferous or broadleaved tree species. This implies that as soon as one tree species dominates, the risk reduction factor becomes lower. Coppice forests showed the lowest variability in hazard reduction. Hazard reduction due to forests increases, on average, by 7% for an increase in the stem number by 100 stems per hectare. The proposed concept allows a global view of the effectiveness of protective forests against rockfall processes and thus enable to value forest ecosystem services for future transregional assessments on a European level. Based on our results, general cost–benefit considerations of nature-based solutions against rockfall, such as protective forests as well as first-order evaluations of rockfall hazard reduction effects of silvicultural measures within the different forest types, can be supported.

In this work we reduce undersampling artefacts in two-dimensional ($2D$) golden-angle radial cine cardiac MRI by applying a modified version of the U-net. We train the network on $2D$ spatio-temporal slices which are previously extracted from the image sequences. We compare our approach to two $2D$ and a $3D$ Deep Learning-based post processing methods and to three iterative reconstruction methods for dynamic cardiac MRI. Our method outperforms the $2D$ spatially trained U-net and the $2D$ spatio-temporal U-net. Compared to the $3D$ spatio-temporal U-net, our method delivers comparable results, but with shorter training times and less training data. Compared to the Compressed Sensing-based methods $kt$-FOCUSS and a total variation regularised reconstruction approach, our method improves image quality with respect to all reported metrics. Further, it achieves competitive results when compared to an iterative reconstruction method based on adaptive regularization with Dictionary Learning and total variation, while only requiring a small fraction of the computational time. A persistent homology analysis demonstrates that the data manifold of the spatio-temporal domain has a lower complexity than the spatial domain and therefore, the learning of a projection-like mapping is facilitated. Even when trained on only one single subject without data-augmentation, our approach yields results which are similar to the ones obtained on a large training dataset. This makes the method particularly suitable for training a network on limited training data. Finally, in contrast to the spatial $2D$ U-net, our proposed method is shown to be naturally robust with respect to image rotation in image space and almost achieves rotation-equivariance where neither data-augmentation nor a particular network design are required., Comment: To be published in IEEE Transactions on Medical Imaging

The concept of sparsity has been extensively applied for regularization in image reconstruction. Typically, sparsifying transforms are either pre-trained on ground-truth images or adaptively trained during the reconstruction. Thereby, learning algorithms are designed to minimize some target function which encodes the desired properties of the transform. However, this procedure ignores the subsequently employed reconstruction algorithm as well as the physical model which is responsible for the image formation process. Iterative neural networks - which contain the physical model - can overcome these issues. In this work, we demonstrate how convolutional sparsifying filters can be efficiently learned by end-to-end training of iterative neural networks. We evaluated our approach on a non-Cartesian 2D cardiac cine MRI example and show that the obtained filters are better suitable for the corresponding reconstruction algorithm than the ones obtained by decoupled pre-training., Accepted at ISBI 2022

Models and simulation tools for gravitational mass flows (GMFs) such as snow avalanches, rockfall, landslides, and debris flows are important for research, education, and practice. In addition to basic simulations and classic applications (e.g., hazard zone mapping), the importance and adaptability of GMF simulation tools for new and advanced applications (e.g., automatic classification of terrain susceptible for GMF initiation or identification of forests with a protective function) are currently driving model developments. In principle, two types of modeling approaches exist: process-based physically motivated and data-based empirically motivated models. The choice for one or the other modeling approach depends on the addressed question, the availability of input data, the required accuracy of the simulation output, and the applied spatial scale. Here we present the computationally inexpensive open-source GMF simulation tool Flow-Py. Flow-Py's model equations are implemented via the Python computer language and based on geometrical relations motivated by the classical data-based runout angle concepts and path routing in three-dimensional terrain. That is, Flow-Py employs a data-based modeling approach to identify process areas and corresponding intensities of GMFs by combining models for routing and stopping, which depend on local terrain and prior movement. The only required input data are a digital elevation model, the positions of starting zones, and a minimum of four model parameters. In addition to the major advantage that the open-source code is freely available for further model development, we illustrate and discuss Flow-Py's key advancements and simulation performance by means of three computational experiments. Implementation and validation. We provide a well-organized and easily adaptable solver and present its application to GMFs on generic topographies. Performance. Flow-Py's performance and low computation time are demonstrated by applying the simulation tool to a case study of snow avalanche modeling on a regional scale. Modularity and expandability. The modular and adaptive Flow-Py development environment allows access to spatial information easily and consistently, which enables, e.g., back-tracking of GMF paths that interact with obstacles to their starting zones. The aim of this contribution is to enable the reader to reproduce and understand the basic concepts of GMF modeling at the level of (1) derivation of model equations and (2) their implementation in the Flow-Py code. Therefore, Flow-Py is an educational, innovative GMF simulation tool that can be applied for basic simulations but also for more sophisticated and custom applications such as identifying forests with a protective function or quantifying effects of forests on snow avalanches, rockfall, landslides, and debris flows.

PURPOSE Iterative convolutional neural networks (CNNs) which resemble unrolled learned iterative schemes have shown to consistently deliver state-of-the-art results for image reconstruction problems across different imaging modalities. However, because these methods include the forward model in the architecture, their applicability is often restricted to either relatively small reconstruction problems or to problems with operators which are computationally cheap to compute. As a consequence, they have not been applied to dynamic non-Cartesian multi-coil reconstruction problems so far. METHODS In this work, we propose a CNN architecture for image reconstruction of accelerated 2D radial cine MRI with multiple receiver coils. The network is based on a computationally light CNN component and a subsequent conjugate gradient (CG) method which can be jointly trained end-to-end using an efficient training strategy. We investigate the proposed training strategy and compare our method with other well-known reconstruction techniques with learned and non-learned regularization methods. RESULTS Our proposed method outperforms all other methods based on non-learned regularization. Further, it performs similar or better than a CNN-based method employing a 3D U-Net and a method using adaptive dictionary learning. In addition, we empirically demonstrate that even by training the network with only iteration, it is possible to increase the length of the network at test time and further improve the results. CONCLUSIONS End-to-end training allows to highly reduce the number of trainable parameters of and stabilize the reconstruction network. Further, because it is possible to change the length of the network at the test time, the need to find a compromise between the complexity of the CNN-block and the number of iterations in each CG-block becomes irrelevant.

PURPOSE In the past, dictionary learning (DL) and sparse coding (SC) have been proposed for the regularization of image reconstruction problems. The regularization is given by a sparse approximation of all image patches using a learned dictionary, that is, an overcomplete set of basis functions learned from data. Despite its competitiveness, DL and SC require the tuning of two essential hyperparameters: the sparsity level S - the number of basis functions of the dictionary, called atoms, which are used to approximate each patch, and K - the overall number of such atoms in the dictionary. These two hyperparameters usually have to be chosen a priori and are determined by repetitive and computationally expensive experiments. Furthermore, the final reported values vary depending on the specific situation. As a result, the clinical application of the method is limited, as standardized reconstruction protocols have to be used. METHODS In this work, we use adaptive DL and propose a novel adaptive sparse coding algorithm for two-dimensional (2D) radial cine MR image reconstruction. Using adaptive DL and adaptive SC, the optimal dictionary size K as well as the optimal sparsity level S are chosen dependent on the considered data. RESULTS Our three main results are the following: First, adaptive DL and adaptive SC deliver results which are comparable or better than the most widely used nonadaptive version of DL and SC. Second, the time needed for the regularization is accelerated due to the fact that the sparsity level S is never overestimated. Finally, the a priori choice of S and K is no longer needed but is optimally chosen dependent on the data under consideration. CONCLUSIONS Adaptive DL and adaptive SC can highly facilitate the application of DL- and SC-based regularization methods. While in this work we focused on 2D radial cine MR image reconstruction, we expect the method to be applicable to different imaging modalities as well.

Cardiac imaging has a pivotal role in the prevention, diagnosis and treatment of ischaemic heart disease. SPECT is most commonly used for clinical myocardial perfusion imaging, whereas PET is the clinical reference standard for the quantification of myocardial perfusion. MRI does not involve exposure to ionizing radiation, similar to echocardiography, which can be performed at the bedside. CT perfusion imaging is not frequently used but CT offers coronary angiography data, and invasive catheter-based methods can measure coronary flow and pressure. Technical improvements to the quantification of pathophysiological parameters of myocardial ischaemia can be achieved. Clinical consensus recommendations on the appropriateness of each technique were derived following a European quantitative cardiac imaging meeting and using a real-time Delphi process. SPECT using new detectors allows the quantification of myocardial blood flow and is now also suited to patients with a high BMI. PET is well suited to patients with multivessel disease to confirm or exclude balanced ischaemia. MRI allows the evaluation of patients with complex disease who would benefit from imaging of function and fibrosis in addition to perfusion. Echocardiography remains the preferred technique for assessing ischaemia in bedside situations, whereas CT has the greatest value for combined quantification of stenosis and characterization of atherosclerosis in relation to myocardial ischaemia. In patients with a high probability of needing invasive treatment, invasive coronary flow and pressure measurement is well suited to guide treatment decisions. In this Consensus Statement, we summarize the strengths and weaknesses as well as the future technological potential of each imaging modality., Cardiac imaging has a pivotal role in the prevention, diagnosis and treatment of ischaemic heart disease. In this Consensus Statement, the authors summarize the use of SPECT, PET, MRI, echocardiography, CT and invasive coronary flow and pressure measurement, and describe the relative strengths and weaknesses of each modality.

Simulation tools for gravitational mass flows (e.g., avalanches, debris flows) are commonly used for research and applications in hazard assessment or mitigation planning. As a basis for a transparent and reproducible decision making process, associated uncertainties need to be identified in order to quantify and eventually communicate the associated variabilities of the results. Main sources of variabilities in the simulation results are associated with parameter variations arising from observation and model uncertainties. These are connected to the measurement inaccuracies or poor process understanding and the numerical model implementation. Probabilistic approaches provide various theoretical concepts to treat these uncertainties, but their direct application is not straightforward. To provide a comprehensive tool, introducing conditional runout probabilities for the decision making process we (i) introduce a mathematical framework based on well-established Bayesian concepts, (ii) develop a work flow that couples this framework to the existing simulation tool r.avaflow, and (iii) apply the work flow to two case studies, highlighting its application potential and limitations. The presented approach allows for back, forward and predictive calculations. Back calculations are used to determine parameter distributions, identifying and mapping the model, implementation and data uncertainties. These parameter distributions serve as a base for forward and predictive calculations, embedded in the probabilistic framework. The result variability is quantified in terms of conditional probabilities with respect to the observed data and the associated simulation and data uncertainties. To communicate the result variability the conditional probabilities are visualized, allowing to identify areas with large or small result variability. The conditional probabilities are particularly interesting for predictive avalanche simulations at locations with no prior information where visualization explicitly shows the result variabilities based on parameter distributions derived through back calculations from locations with well-documented observations.

In this paper, we combine deterministic splitting methods with a polynomial chaos expansion method for solving stochastic parabolic evolution problems. The stochastic differential equation is reduced to a system of deterministic equations that we solve explicitly by splitting methods. The method can be applied to a wide class of problems where the related stochastic processes are given uniquely in terms of stochastic polynomials. A comprehensive convergence analysis is provided and numerical experiments validate our approach., Comment: 28 pages, 3 figures, 1 table

In this paper we present a generalized Deep Learning-based approach for solving ill-posed large-scale inverse problems occuring in medical image reconstruction. Recently, Deep Learning methods using iterative neural networks (NNs) and cascaded NNs have been reported to achieve state-of-the-art results with respect to various quantitative quality measures as PSNR, NRMSE and SSIM across different imaging modalities. However, the fact that these approaches employ the application of the forward and adjoint operators repeatedly in the network architecture requires the network to process the whole images or volumes at once, which for some applications is computationally infeasible. In this work, we follow a different reconstruction strategy by strictly separating the application of the NN, the regularization of the solution and the consistency with the measured data. The regularization is given in the form of an image prior obtained by the output of a previously trained NN which is used in a Tikhonov regularization framework. By doing so, more complex and sophisticated network architectures can be used for the removal of the artefacts or noise than it is usually the case in iterative NNs. Due to the large scale of the considered problems and the resulting computational complexity of the employed networks, the priors are obtained by processing the images or volumes as patches or slices. We evaluated the method for the cases of 3D cone-beam low dose CT and undersampled 2D radial cine MRI and compared it to a total variation-minimization-based reconstruction algorithm as well as to a method with regularization based on learned overcomplete dictionaries. The proposed method outperformed all the reported methods with respect to all chosen quantitative measures and further accelerates the regularization step in the reconstruction by several orders of magnitude.

Snow avalanche simulation software is a commonly used tool for hazard estimation and mitigation planning. In this study a depth-averaged flow model, combining a simple entrainment and friction relation, is implemented in the software SamosAT. Computational results strongly depend on the simulation input, in particular on the employed model parameters. A long-standing problem is to quantify the influence of these parameters on the simulation results. We present a new multivariate optimization approach for avalanche simulation in three-dimensional terrain. The method takes into account the entire physically relevant range of the two friction parameters (Coulomb friction, turbulent drag) and one entrainment parameter. These three flow model parameters are scrutinized with respect to six optimization variables (runout, matched and exceeded affected area, maximum velocity, average deposition depth and mass growth). The approach is applied to a documented extreme avalanche event, recorded in St Anton, Austria. The final results provide adjusted parameter distributions optimizing the simulation–observation correspondence. At the same time, the degree of parameter–variable correspondence is determined. We show that the specification of optimal values for certain model parameters is near-impossible, if corresponding optimization variables are neglected or unavailable.

Objective: To evaluate the efficacy and safety of simplified maintenance therapy (SMT) compared with continued protease inhibitor (PI) therapy. Design: Meta-analysis of nine randomized controlled trials in which 833 patients were switched to SMT (abacavir, efavirenz or nevirapine) and 616 continued PI, assessing virologic failure (primary outcome), discontinuation of therapy for reasons other than virologic failure, CD4 cell count, total plasma cholesterol and triglycerides. Results: The risk ratio for virologic failure for SMT compared to continued PI was 1.06 [95% confidence interval (Cl) 0.58-1.92; test for homogeneity P = 0.01] for SMT, 2.56, (95% Cl, 1.17-5.64) for abacavir, 0.83 (95% Cl, 0.36-1.91) for efavirenz and 0.54 (95% Cl, 0.29-1.02) for nevirapine. The risk ratio for premature discontinuation of therapy with SMT was 0.61 (95% Cl, 0.48-0.77; test for homogeneity P < 0.10). The difference in absolute mean cholesterol for SMT compared to continued PI was -0.15 mmol/l, (95% Cl, -0.40 to 0.09; test for homogeneity P < 0.01) for SMT, -0.51 mmol/l (95% Cl, -0.70 to -0.33) for abacavir, 0.22 mmol/l (95% Cl, 0 to 0.43) for efavirenz and -0.19 mmol/l (95% Cl, -0.48 to 0.09) for nevirapine. Conclusions: Current evidence suggests that SMT with abacavir rather than continued PI increases the risk of virologic failure, this increased risk may be confined to patients with prior mono or dual therapy with reverse transcriptase inhibitors. There is not enough evidence on whether SMT with efavirenz and nevirapine influences the risk of virologic failure. SMT with any of the three drugs reduces the risk of discontinuation of therapy, and SMTwith abacavir reduces plasma cholesterol.

Background: Persons infected with human immunodefi ciency virus (HIV) have an increased risk for several cancers, but the infl uences of behavioral risk factors, such as smoking and intravenous drug use, and highly active antiretroviral therapy (HAART) on cancer risk are not clear. Methods: Patient records were linked between the Swiss HIV Cohort Study and Swiss cantonal cancer registries. Observed and expected numbers of incident cancers were assessed in 7304 persons infected with HIV followed for 28 836 person-years. Relative risks for cancer compared with those for the general population were determined by estimating cancer registry – , sex-, age-, and period-standardized incidence ratios (SIRs). Results: Highly elevated SIRs were confi rmed in persons infected with HIV for Kaposi sarcoma (KS) (SIR = 192, 95% confi dence interval [CI] = 170 to 217) and non-Hodgkin lymphoma (SIR = 76.4, 95% CI = 66.5 to 87.4). Statistically signifi cantly elevated SIRs were also observed for anal cancer (SIR = 33.4, 95% CI = 10.5 to 78.6); Hodgkin lymphoma (SIR = 17.3, 95% CI = 10.2 to 27.4); cancers of the cervix (SIR = 8.0, 95% CI = 2.9 to 17.4); liver (SIR = 7.0, 95% CI = 2.2 to 16.5); lip, mouth, and pharynx (SIR = 4.1, 95% CI = 2.1 to 7.4); trachea, lung, and bronchus (SIR = 3.2, 95% CI = 1.7 to 5.4); and skin, nonmelanomatous (SIR = 3.2, 95% CI = 2.2 to 4.5). In HAART users, SIRs for KS (SIR = 25.3, 95% CI = 10.8 to 50.1) and non-Hodgkin lymphoma (SIR = 24.2, 95% CI = 15.0 to 37.1) were lower than those for nonusers (KS SIR = 239, 95% CI = 211 to 270; non-Hodgkin lymphoma SIR = 99.3, 95% CI = 85.8 to 114). Among HAART users, however, the SIR (although not absolute numbers) for Hodgkin lymphoma (SIR = 36.2, 95% CI = 16.4 to 68.9) was comparable to that for KS and non-Hodgkin lymphoma. No clear impact of HAART on SIRs emerged for cervical cancer or non – acquired immunodefi ciency syndrome-defi ning cancers. Cancers of the lung, lip, mouth, or pharynx were not observed among nonsmokers. Conclusion: In persons infected with HIV, HAART use may prevent most excess risk of KS and non-Hodgkin lymphoma, but not that of Hodgkin lymphoma and other non – acquired immunodefi ciency syndrome-defi ning cancers. No cancers of the lip, mouth, pharynx, or lung were observed in nonsmokers. [J Natl Cancer Inst 2005;97:425 – 32]