Erich Kobler

Bio: Erich Kobler is an academic researcher from Graz University of Technology. The author has contributed to research in topics: Computer science & Iterative reconstruction. The author has an hindex of 8, co-authored 27 publications receiving 1202 citations. Previous affiliations of Erich Kobler include Johannes Kepler University of Linz.

Learning a variational network for reconstruction of accelerated MRI data.

Abstract: 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.

Learning a Variational Network for Reconstruction of Accelerated MRI Data

Abstract: 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. The variational network reconstructions outperform standard reconstruction algorithms in terms of image quality and residual artifacts for all tested acceleration factors and sampling patterns. 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, i.e., 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.

Assessment of the generalization of learned image reconstruction and the potential for transfer learning

Abstract: 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.

Variational Networks: Connecting Variational Methods and Deep Learning

Abstract: 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.

Total Deep Variation for Linear Inverse Problems

Abstract: 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.

Image reconstruction by domain-transform manifold learning

Abstract: 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.

All-optical machine learning using diffractive deep neural networks

Abstract: 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.

Learning a variational network for reconstruction of accelerated MRI data.

Abstract: 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.

Regularization Of Inverse Problems

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RAFT: Recurrent All-Pairs Field Transforms for Optical Flow

Abstract: 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.