Image reconstruction is essential for imaging applications across the physical and life sciences, including optical and radar systems, magnetic resonance imaging, X-ray computed tomography, positron emission tomography, ultrasound imaging and radio astronomy. During image acquisition, the sensor encodes an intermediate representation of an object in the sensor domain, which is subsequently reconstructed into an image by an inversion of the encoding function. Image reconstruction is challenging because analytic knowledge of the exact inverse transform may not exist a priori, especially in the presence of sensor non-idealities and noise. Thus, the standard reconstruction approach involves approximating the inverse function with multiple ad hoc stages in a signal processing chain, the composition of which depends on the details of each acquisition strategy, and often requires expert parameter tuning to optimize reconstruction performance. Here we present a unified framework for image reconstruction-automated transform by manifold approximation (AUTOMAP)-which recasts image reconstruction as a data-driven supervised learning task that allows a mapping between the sensor and the image domain to emerge from an appropriate corpus of training data. We implement AUTOMAP with a deep neural network and exhibit its flexibility in learning reconstruction transforms for various magnetic resonance imaging acquisition strategies, using the same network architecture and hyperparameters. We further demonstrate that manifold learning during training results in sparse representations of domain transforms along low-dimensional data manifolds, and observe superior immunity to noise and a reduction in reconstruction artefacts compared with conventional handcrafted reconstruction methods. In addition to improving the reconstruction performance of existing acquisition methodologies, we anticipate that AUTOMAP and other learned reconstruction approaches will accelerate the development of new acquisition strategies across imaging modalities.

Image reconstruction by domain-transform manifold learning

Deep learning has been transforming our ability to execute advanced inference tasks using computers. Here we introduce a physical mechanism to perform machine learning by demonstrating an all-optical diffractive deep neural network (D2NN) architecture that can implement various functions following the deep learning-based design of passive diffractive layers that work collectively. We created 3D-printed D2NNs that implement classification of images of handwritten digits and fashion products, as well as the function of an imaging lens at a terahertz spectrum. Our all-optical deep learning framework can perform, at the speed of light, various complex functions that computer-based neural networks can execute; will find applications in all-optical image analysis, feature detection, and object classification; and will also enable new camera designs and optical components that perform distinctive tasks using D2NNs.

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All-optical machine learning using diffractive deep neural networks

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.

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Learning a variational network for reconstruction of accelerated MRI data.

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Regularization Of Inverse Problems

We introduce Recurrent All-Pairs Field Transforms (RAFT), a new deep network architecture for optical flow. RAFT extracts per-pixel features, builds multi-scale 4D correlation volumes for all pairs of pixels, and iteratively updates a flow field through a recurrent unit that performs lookups on the correlation volumes. RAFT achieves state-of-the-art performance. On KITTI, RAFT achieves an F1-all error of 5.10%, a 16% error reduction from the best published result (6.10%). On Sintel (final pass), RAFT obtains an end-point-error of 2.855 pixels, a 30% error reduction from the best published result (4.098 pixels). In addition, RAFT has strong cross-dataset generalization as well as high efficiency in inference time, training speed, and parameter count. Code is available at https://github.com/princeton-vl/RAFT.

RAFT: Recurrent All-Pairs Field Transforms for Optical Flow

Objectives 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. Materials and Methods 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. Results 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 = <0.001; 5-minute: −0.93 ± 0.91, P = <0.001; extended: −0.96 ± 0.97, P = <0.001; zero-dose: −2.39 ± 1.14, P = <0.001). The average scores of conformity of the lesions compared with the original full-dose sequence were 2.25 ± 1.21, 2.22 ± 1.27, 2.24 ± 1.25, and 0.73 ± 0.93 for the standard, 5-minute, extended, and zero-dose setting, respectively. Conclusions The tested deep learning algorithm for synthesis of artificial T1w full-dose sequences based on images after administration of only 10% of the standard dose of a gadolinium-based contrast agent showed very good quantitative performance. Despite good image quality in all settings, both false-negative and false-positive signals resulted in significantly limited interchangeability of the synthesized sequences with the original full-dose sequences.

Reduction of Gadolinium-Based Contrast Agents in MRI Using Convolutional Neural Networks and Different Input Protocols

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.

Total Deep Variation for Noisy Exit Wave Reconstruction in Transmission Electron Microscopy

Abstract Deep learning approaches are playing an ever-increasing role throughout diagnostic medicine, especially in neuroradiology, to solve a wide range of problems such as segmentation, synthesis of missing sequences, and image quality improvement. Of particular interest is their application in the reduction of gadolinium-based contrast agents, the administration of which has been under cautious reevaluation in recent years because of concerns about gadolinium deposition and its unclear long-term consequences. A growing number of studies are investigating the reduction (low-dose approach) or even complete substitution (zero-dose approach) of gadolinium-based contrast agents in diverse patient populations using a variety of deep learning methods. This work aims to highlight selected research and discusses the advantages and limitations of recent deep learning approaches, the challenges of assessing its output, and the progress toward clinical applicability distinguishing between the low-dose and zero-dose approach.

Artificial Contrast

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 modelling 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. As a result, we obtain highly efficient numerical schemes that achieve competitive results for image denoising and image deblurring. A nonlinear spectral analysis of the gradient of the learned regularizer gives enlightening insights about the different regularization properties.

An Optimal Control Approach to Early Stopping Variational Methods for Image Restoration.

In this paper, we propose a unified framework of denoising score-based models in the context of graduated non-convex energy minimization. We show that for sufficiently large noise variance, the associated negative log density -- the energy -- becomes convex. Consequently, denoising score-based models essentially follow a graduated non-convexity heuristic. We apply this framework to learning generalized Fields of Experts image priors that approximate the joint density of noisy images and their associated variances. These priors can be easily incorporated into existing optimization algorithms for solving inverse problems and naturally implement a fast and robust graduated non-convexity mechanism.

Erich Kobler

Papers

Reduction of Gadolinium-Based Contrast Agents in MRI Using Convolutional Neural Networks and Different Input Protocols

Total Deep Variation for Noisy Exit Wave Reconstruction in Transmission Electron Microscopy

Artificial Contrast

An Optimal Control Approach to Early Stopping Variational Methods for Image Restoration.

Learning Gradually Non-convex Image Priors Using Score Matching