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The purpose of this study was to implement a state-of-the-art convolutional neural network used to synthesize artificial T1-weighted (T1w) full-dose images from corresponding noncontrast and low-dose images (using various settings of input sequences) and test its performance on a patient population acquired prospectively.In this monocentric, institutional review board-approved study, a total of 138 participants were included who received an adapted imaging protocol with acquisition of a T1w low dose after administration of 10% of the standard dose and acquisition of a T1w full dose after administration of the remaining 90% of the standard dose of a gadolinium-containing contrast agent. A total of 83 participants formed the training sample (51.7 ± 16.5 years, 36 women), 25 the validation sample (55.3 ± 16.4 years, 11 women), and 30 the test sample (55.0 ± 15.0 years, 9 women). Four input settings were differentiated: only the T1w noncontrast and T1w low-dose images (standard setting), only the T1w noncontrast and T1w low-dose images with a prolonged postinjection time of 5 minutes (5-minute setting), multiple noncontrast sequences (T1w, T2w, diffusion) and the T1w low-dose images (extended setting), and only noncontrast sequences (T1w, T2w, diffusion) were used (zero-dose setting). For each setting, a deep neural network was trained to synthesize artificial T1w full-dose images, which were assessed on the test sample using an objective evaluation based on quantitative metrics and a subjective evaluation through a reader-based study. Three readers scored the overall image quality, the interchangeability in regard to the clinical conclusion compared with the true T1w full-dose sequence, the contrast enhancement of lesions, and their conformity to the respective references in the true T1w full dose.Quantitative analysis of the artificial T1w full-dose images of the standard setting provided a peak signal-to-noise ratio of 33.39 ± 0.62 (corresponding to an average improvement of the low-dose sequences of 5.2 dB) and a structural similarity index measure of 0.938 ± 0.005. In the 4-fold cross-validation, the extended setting yielded similar performance to the standard setting in terms of peak signal-to-noise ratio ( P = 0.20), but a slight improvement in structural similarity index measure ( P < 0.0001). For all settings, the reader study found comparable overall image quality between the original and artificial T1w full-dose images. The proportion of scans scored as fully or mostly interchangeable was 55%, 58%, 43%, and 3% and the average counts of false positives per case were 0.42 ± 0.83, 0.34 ± 0.71, 0.82 ± 1.15, and 2.00 ± 1.07 for the standard, 5-minute, extended, and zero-dose setting, respectively. Using a 5-point Likert scale (0 to 4, 0 being the worst), all settings of synthesized full-dose images showed significantly poorer contrast enhancement of lesions compared with the original full-dose sequence (difference of average degree of contrast enhancement-standard: -0.97 ± 0.83, P =

We propose a novel learning-based framework for image reconstruction particularly designed for training without ground truth data, which has three major building blocks: energy-based learning, a patch-based Wasserstein loss functional, and shared prior learning. In energy-based learning, the parameters of an energy functional composed of a learned data fidelity term and a data-driven regularizer are computed in a mean-field optimal control problem. In the absence of ground truth data, we change the loss functional to a patch-based Wasserstein functional, in which local statistics of the output images are compared to uncorrupted reference patches. Finally, in shared prior learning, both aforementioned optimal control problems are optimized simultaneously with shared learned parameters of the regularizer to further enhance unsupervised image reconstruction. We derive several time discretization schemes of the gradient flow and verify their consistency in terms of Mosco convergence. In numerous numerical experiments, we demonstrate that the proposed method generates state-of-the-art results for various image reconstruction applications--even if no ground truth images are available for training., 37 pages, 19 figures

We investigate a well-known phenomenon of variational approaches in image processing, where typically the best image quality is achieved when the gradient flow process is stopped before converging to a stationary point. This paradox originates from a tradeoff between optimization and modeling errors of the underlying variational model and holds true even if deep learning methods are used to learn highly expressive regularizers from data. In this paper, we take advantage of this paradox and introduce an optimal stopping time into the gradient flow process, which in turn is learned from data by means of an optimal control approach. After a time discretization, we obtain variational networks, which can be interpreted as a particular type of recurrent neural networks. The learned variational networks achieve competitive results for image denoising and image deblurring on a standard benchmark data set. One of the key theoretical results is the development of first- and second-order conditions to verify optimal stopping time. A nonlinear spectral analysis of the gradient of the learned regularizer gives enlightening insights into the different regularization properties.

Electron tomography allows one to obtain 3D reconstructions visualizing a tissue’s ultrastructure from a series of 2D projection images. An inherent problem with this imaging technique is that its projection images contain unwanted shifts, which must be corrected for to achieve reliable reconstructions. Commonly, the projection images are aligned with each other by means of fiducial markers prior to the reconstruction procedure. In this work, we propose a joint alignment and reconstruction algorithm that iteratively solves for both the unknown reconstruction and the unintentional shift and does not require any fiducial markers. We evaluate the approach first on synthetic phantom data where the focus is not only on the reconstruction quality but more importantly on the shift correction. Subsequently, we apply the algorithm to healthy C57BL/6J mice and then compare it with non-obese diabetic (NOD) mice, with the aim of visualizing the attack of immune cells on pancreatic beta cells within type 1 diabetic mice at a more profound level through 3D analysis. We empirically demonstrate that the proposed algorithm is able to compute the shift with a remaining error at only the sub-pixel level and yields high-quality reconstructions for the limited-angle inverse problem. By decreasing labour and material costs, the algorithm facilitates further research directed towards investigating the immune system’s attacks in pancreata of NOD mice for numerous samples at different stages of type 1 diabetes.

Deep Image Prior (DIP) is currently among the most efficient unsupervised deep learning based methods for ill-posed inverse problems in imaging. This novel framework relies on the implicit regularization provided by representing images as the output of generative Convolutional Neural Network (CNN) architectures. So far, DIP has been shown to be an effective approach when combined with classical and novel regularizers. Unfortunately, to obtain appropriate solutions, all the models proposed up to now require an accurate estimate of the regularization parameter. To overcome this difficulty, we consider a locally adapted regularized unconstrained model whose local regularization parameters are automatically estimated for additively separable regularizers. Moreover, we propose a novel constrained formulation in analogy to Morozov's discrepancy principle which enables the application of a broader range of regularizers. Both the unconstrained and the constrained models are solved via the proximal gradient descent-ascent method. Numerical results demonstrate the robustness with respect to image content, noise levels and hyperparameters of the proposed models on both denoising and deblurring of simulated as well as real natural and medical images.

Recent deep learning approaches focus on improving quantitative scores of dedicated benchmarks, and therefore only reduce the observation-related (aleatoric) uncertainty. However, the model-immanent (epistemic) uncertainty is less frequently systematically analyzed. In this work, we introduce a Bayesian variational framework to quantify the epistemic uncertainty. To this end, we solve the linear inverse problem of undersampled MRI reconstruction in a variational setting. The associated energy functional is composed of a data fidelity term and the total deep variation (TDV) as a learned parametric regularizer. To estimate the epistemic uncertainty we draw the parameters of the TDV regularizer from a multivariate Gaussian distribution, whose mean and covariance matrix are learned in a stochastic optimal control problem. In several numerical experiments, we demonstrate that our approach yields competitive results for undersampled MRI reconstruction. Moreover, we can accurately quantify the pixelwise epistemic uncertainty, which can serve radiologists as an additional resource to visualize reconstruction reliability., Comment: 19 pages, 11 figures

Transmission electron microscopes (TEMs) are ubiquitous devices for high-resolution imaging on an atomic level. A key problem related to TEMs is the reconstruction of the exit wave, which is the electron signal at the exit plane of the examined specimen. Frequently, this reconstruction is cast as an ill-posed nonlinear inverse problem. In this work, we integrate the data-driven total deep variation regularizer to reconstruct the exit wave in this inverse problem. In several numerical experiments, the applicability of the proposed method is demonstrated for different materials.

This paper combines image metamorphosis with deep features. To this end, images are considered as maps into a high-dimensional feature space and a structure-sensitive, anisotropic flow regularization is incorporated in the metamorphosis model proposed by Miller, Trouv\'e, Younes and coworkers. For this model a variational time discretization of the Riemannian path energy is presented and the existence of discrete geodesic paths minimizing this energy is demonstrated. Furthermore, convergence of discrete geodesic paths to geodesic paths in the time continuous model is investigated. The spatial discretization is based on a finite difference approximation in image space and a stable spline approximation in deformation space, the fully discrete model is optimized using the iPALM algorithm. Numerical experiments indicate that the incorporation of semantic deep features is superior to intensity-based approaches., Comment: 26 pages, 5 figures; This publication is an extended version of the previous conference proceeding presented at SSVM 2019

Diverse inverse problems in imaging can be cast as variational problems composed of a task-specific data fidelity term and a regularization term. In this paper, we propose a novel learnable general-purpose regularizer exploiting recent architectural design patterns from deep learning. We cast the learning problem as a discrete sampled optimal control problem, for which we derive the adjoint state equations and an optimality condition. By exploiting the variational structure of our approach, we perform a sensitivity analysis with respect to the learned parameters obtained from different training datasets. Moreover, we carry out a nonlinear eigenfunction analysis, which reveals interesting properties of the learned regularizer. We show state-of-the-art performance for classical image restoration and medical image reconstruction problems., Comment: 21 pages, 10 figures

PURPOSE To allow fast and high-quality reconstruction of clinical accelerated multi-coil MR data by learning a variational network that combines the mathematical structure of variational models with deep learning. THEORY AND METHODS Generalized compressed sensing reconstruction formulated as a variational model is embedded in an unrolled gradient descent scheme. All parameters of this formulation, including the prior model defined by filter kernels and activation functions as well as the data term weights, are learned during an offline training procedure. The learned model can then be applied online to previously unseen data. RESULTS The variational network approach is evaluated on a clinical knee imaging protocol for different acceleration factors and sampling patterns using retrospectively and prospectively undersampled data. The variational network reconstructions outperform standard reconstruction algorithms, verified by quantitative error measures and a clinical reader study for regular sampling and acceleration factor 4. CONCLUSION Variational network reconstructions preserve the natural appearance of MR images as well as pathologies that were not included in the training data set. Due to its high computational performance, that is, reconstruction time of 193 ms on a single graphics card, and the omission of parameter tuning once the network is trained, this new approach to image reconstruction can easily be integrated into clinical workflow. Magn Reson Med 79:3055-3071, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Image morphing in computer vision amounts to computing a visually appealing transition of two images. A prominent model for image morphing originally proposed by Trouve, Younes and coworkers is image metamorphosis. Here, the space of images is endowed with a Riemannian metric that separately quantifies the contributions due to transport and image intensity variations along a transport path. Geodesic curves in this Riemannian space of images give rise to morphing transitions. The classical metamorphosis model considers images as square-integrable functions on some image domain and thus is non-sensitive to image features such as sharp interfaces or fine texture patterns. To resolve this drawback, we treat images not as intensity maps, but rather as maps into some feature space that encode local structure information. In the simplest case, color intensities are such feature vectors. To appropriately treat local structures and semantic information, deep convolutional neural network features are investigated. The resulting model is formulated directly in terms of a variational time discretization developed for the classical metamorphosis model by Berkels, Effland and Rumpf. The key ingredient is a mismatch energy that locally approximates the squared Riemannian distance and consists of a regularization energy of the time discrete flow and a dissimilarity energy that measures the feature vector modulation along discrete transport paths. The spatial discretization is based on a finite difference and a stable spline interpolation. A variety of numerical examples demonstrates the robustness and versatility of the proposed method for real images using a variant of the iPALM algorithm for the minimization of the fully discrete energy functional.

Magnetic resonance imaging is a leading image modality for many clinical applications; however, a significant drawback is the lengthy data acquisition. This motivates the development of methods for reconstruction of sparsely sampled image data. One such technique is the Variational Network (VN), a machine learning method that generalizes traditional iterative reconstruction techniques, learning the regularization term from large amounts of image data. Previously, with the VN technique, reconstruction of 4-fold accelerated knee images was shown to be highly successful. In this work we extend the VN approach to applications beyond knee imaging and evaluate the classic VN and a newly developed Unet-VN in 5 different anatomical regions. We evaluate the networks trained individually for each anatomical area as well as jointly trained with data from all anatomical areas. The VN and Unet-VN were trained to reconstruct 4-fold accelerated images of knees, brains, hips, ankles and shoulders. SSIM was calculated to quantitatively evaluate the reconstructed images. Results show that the Unet-VN outperforms the classic VN, both quantitatively – in terms of structural similarity – and qualitatively. The networks jointly trained with multi-anatomy data approach the performance of the individually trained networks and offer the simplicity of a single network for a range of clinical applications which has substantial benefit for clinical translation.

PURPOSE: To investigate the feasibility of accelerating prostate diffusion-weighted imaging (DWI) by reducing the number of acquired averages and denoising the resulting image using a proposed guided denoising convolutional neural network (DnCNN). MATERIALS AND METHODS: Raw data from the prostate DWI scans were retrospectively gathered between July 2018 and July 2019 from six single-vendor MRI scanners. There were 103 datasets used for training (median age, 64 years; interquartile range [IQR], 11), 15 for validation (median age, 68 years; IQR, 12), and 37 for testing (median age, 64 years; IQR, 12). High b-value diffusion-weighted (hb DW) data were reconstructed into noisy images using two averages and reference images using all 16 averages. A conventional DnCNN was modified into a guided DnCNN, which uses the low b-value DW image as a guidance input. Quantitative and qualitative reader evaluations were performed on the denoised hb DW images. A cumulative link mixed regression model was used to compare the readers’ scores. The agreement between the apparent diffusion coefficient (ADC) maps (denoised vs reference) was analyzed using Bland-Altman analysis. RESULTS: Compared with the original DnCNN, the guided DnCNN produced denoised hb DW images with higher peak signal-to-noise ratio (32.79 ± 3.64 [standard deviation] vs 33.74 ± 3.64), higher structural similarity index (0.92 ± 0.05 vs 0.93 ± 0.04), and lower normalized mean square error (3.9% ± 10 vs 1.6% ± 1.5) (P < .001 for all). Compared with the reference images, the denoised images received higher image quality scores from the readers (P < .0001). The ADC values based on the denoised hb DW images were in good agreement with the reference ADC values (mean ADC difference ranged from −0.04 to 0.02 × 10(-3) mm(2)/sec). CONCLUSION: Accelerating prostate DWI by reducing the number of acquired averages and denoising the resulting image using the proposed guided DnCNN is technically feasible. Supplemental material is available for this article. © RSNA, 2020

Purpose SparseCT, an undersampling scheme for compressed sensing (CS) computed tomography (CT), has been proposed to reduce radiation dose by acquiring undersampled projection data from clinical CT scanners (Koesters et al. in, SparseCT: Interrupted-Beam Acquisition and Sparse Reconstruction for Radiation Dose Reduction; 2017). SparseCT partially blocks the x-ray beam with a multislit collimator (MSC) to perform a multidimensional undersampling along the view and detector row dimensions. SparseCT undersamples the projection data within each view and moves the MSC along the z-direction during gantry rotation to change the undersampling pattern. It enables reconstruction of images from undersampled data using CS algorithms. The purpose of this work is to design the spacing and width of the MSC slits and the MSC motion patterns based on beam separation, undersampling efficiency, and image quality. The development and testing of a SparseCT prototype with the designed MSC will be described in a following paper. Methods We chose a few initial MSC designs based on the guidance from two metrics: beam separation and undersampling efficiency. Both beam separation and undersampling efficiency were measured from numerically simulated photon distribution with MSC taken into consideration. Beam separation measures the separation between x-ray beams from consecutive slits, taking into account penumbra effects on both sides of each slit. Undersampling efficiency measures the dose-weighted similarity between penumbra undersampling and binary undersampling, in other words, the effective contribution of the incident dose to the signal to noise ratio of the projection data. We then compared the initially chosen MSC designs in terms of their reconstruction image quality. SparseCT projections were simulated from fully sampled patient projection data according to the MSC design and motion pattern, reconstructed iteratively using a sparsity-enforcing penalized weighted least squares cost function with ordered subsets/momentum algorithm, and compared visually and quantitatively. Results Simulated photon distributions indicate that the size of the penumbra is dominated by the size of the focal spot. Therefore, a wider MSC slit and a smaller focal spot lead to increased beam separation and undersampling efficiency. For fourfold undersampling with a 1.2 mm focal spot, a minimum MSC slit width of three detector rows (projected to the detector surface) is needed for beam separation; for threefold undersampling, a minimum slit width of four detector rows is needed. Simulations of SparseCT projection and reconstruction indicate that the motion pattern of the MSC does not have a visible impact on image quality. An MSC slit width of three or four detector rows yields similar image quality. Conclusion The MSC is the key component of the SparseCT method. Simulations of MSC designs incorporating x-ray beam penumbra effects showed that for threefold and fourfold dose reductions, an MSC slit width of four detector rows provided reasonable beam separation, undersampling efficiency, and image quality.

Purpose Cancers are almost always diagnosed by morphologic features in tissue sections. In this context, machine learning tools provide new opportunities to describe tumor immune cell interactions within the tumor microenvironment and thus provide phenotypic information that might be predictive for the response to immunotherapy. Methods We develop a machine learning approach using variational networks for joint image denoising and classification of tissue sections for melanoma, which is an established model tumor for immuno-oncology research. The manual annotation of real training data would require substantial user interaction of experienced pathologists for each single training image, and the training of larger networks would rely on a very large number of such data sets with ground truth annotation. To overcome this bottleneck, we synthesize training data together with a proper tissue structure classification. To this end, a stochastic data generation process is used to mimic cell morphology, cell distribution and tissue architecture in the tumor microenvironment. Particular components of this tool are random placement and rotation of a large number of patches for presegmented cell nuclei, a stochastic fast marching approach to mimic the geometry of cells and texture generation based on a color covariance analysis of real data. Here, the generated training data reflect a large range of interaction patterns. Results In several applications to histological tissue sections, we analyze the efficiency and accuracy of the proposed approach. As a result, depending on the scenario considered, almost all cells and nuclei which ought to be detected are actually marked as classified and hardly any misclassifications occur. Conclusions The proposed method allows for a computer-aided screening of histological tissue sections utilizing variational networks with a particular emphasis on tumor immune cell interactions and on the robust cell nuclei classification.

Purpose Although deep learning has shown great promise for MR image reconstruction, an open question regarding the success of this approach is the robustness in the case of deviations between training and test data. The goal of this study is to assess the influence of image contrast, SNR, and image content on the generalization of learned image reconstruction, and to demonstrate the potential for transfer learning. Methods Reconstructions were trained from undersampled data using data sets with varying SNR, sampling pattern, image contrast, and synthetic data generated from a public image database. The performance of the trained reconstructions was evaluated on 10 in vivo patient knee MRI acquisitions from 2 different pulse sequences that were not used during training. Transfer learning was evaluated by fine-tuning baseline trainings from synthetic data with a small subset of in vivo MR training data. Results Deviations in SNR between training and testing led to substantial decreases in reconstruction image quality, whereas image contrast was less relevant. Trainings from heterogeneous training data generalized well toward the test data with a range of acquisition parameters. Trainings from synthetic, non-MR image data showed residual aliasing artifacts, which could be removed by transfer learning-inspired fine-tuning. Conclusion This study presents insights into the generalization ability of learned image reconstruction with respect to deviations in the acquisition settings between training and testing. It also provides an outlook for the potential of transfer learning to fine-tune trainings to a particular target application using only a small number of training cases.

Immunotherapy is currently revolutionizing the treatment of cancer. Detailed analyses of tumor immune cell interaction in the tumor microenvironment will facilitate an accurate prediction of a patient’s clinical response. The automatic and reliable pre-screening of histological tissue sections for tumor infiltrating immune cells (TILs) will support the development of TIL-based predictive biomarkers for checkpoint immunotherapy. In this paper, a learning approach for image classification is presented, which allows various pattern inquires for different types of tissue section images. The underlying trainable reaction diffusion model combines classification and denoising. The model is trained using a stochastic generation of training data. The effectiveness of this approach is demonstrated for immunofluorescent and for Hematoxylin and Eosin (H&E) stained melanoma section images. A particular focus is on the classification of TILs in the proximity to melanoma cells in an experimental melanoma mouse model and in human melanoma. This new learning approach for images of melanoma tissue sections will refine the strategy for the practical clinical application of biomarker research.

In this paper, we introduce variational networks (VNs) for image reconstruction. VNs are fully learned models based on the framework of incremental proximal gradient methods. They provide a natural transition between classical variational methods and state-of-the-art residual neural networks. Due to their incremental nature, VNs are very efficient, but only approximately minimize the underlying variational model. Surprisingly, in our numerical experiments on image reconstruction problems it turns out that giving up exact minimization leads to a consistent performance increase, in particular in the case of convex models.

In this paper, we present a novel method for multi-frame superresolution (SR). Our main goal is to improve the spatial resolution of a multi-line scan camera for an industrial inspection task. High resolution output images are reconstructed using our proposed SR algorithm for multi-channel data, which is based on the trainable reaction-diffusion model. As this is a supervised learning approach, we simulate ground truth data for a real imaging scenario. We show that learning a regularizer for the SR problem improves the reconstruction results compared to an iterative reconstruction algorithm using TV or TGV regularization. We test the learned regularizer, trained on simulated data, on images acquired with the real camera setup and achieve excellent results.

In this work, we propose a learning-based variational network (VN) approach for reconstruction of low-dose 3D computed tomography data. We focus on two methods to decrease the radiation dose: (1) x-ray tube current reduction, which reduces the signal-to-noise ratio, and (2) x-ray beam interruption, which undersamples data and results in images with aliasing artifacts. While the learned VN denoises the current-reduced images in the first case, it reconstructs the undersampled data in the second case. Different VNs for denoising and reconstruction are trained on a single clinical 3D abdominal data set. The VNs are compared against state-of-the-art model-based denoising and sparse reconstruction techniques on a different clinical abdominal 3D data set with 4-fold dose reduction. Our results suggest that the proposed VNs enable higher radiation dose reductions and/or increase the image quality for a given dose.