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

In this paper, we propose a novel method for color propagation that is used to recolor gray-scale videos (e.g. historic movies). Our energy-based model combines deep learning with a variational formulation. At its core, the method optimizes over a set of plausible color proposals that are extracted from motion and semantic feature matches, together with a learned regularizer that resolves color ambiguities by enforcing spatial color smoothness. Our approach allows interpreting intermediate results and to incorporate extensions like using multiple reference frames even after training. We achieve state-of-the-art results on a number of standard benchmark datasets with multiple metrics and also provide convincing results on real historical videos – even though such types of video are not present during training. Moreover, a user evaluation shows that our method propagates initial colors more faithfully and temporally consistent. 

Learned Variational Video Color Propagation

Semi-supervised learning can be a promising approach in expediting the process of annotating medical images. In this paper, we use diffusion models to learn visual representations from multi-modal medical images in an unsupervised setting. These learned representations are then employed for the challenging downstream task of brain tumor segmentation. To avoid feature selection when using pixel-level classifiers, we propose fine-tuning the noise predictor network for semantic segmentation. We compare these methods against a supervised baseline over a varying number of training samples and evaluate their performance on a substantially larger test set. Our results show that, with less than 20 training samples, all methods outperform the supervised baseline across all tumor regions. Additionally, we present a practical use-case for patient-level tumor segmentation using limited supervision. The code we used and our trained diffusion model are publicly available ( https://github.com/risc-mi/braintumor-ddpm ). 

Semi-supervised Brain Tumor Segmentation Using Diffusion Models

Blind Single Image Super-Resolution via Iterated Shared Prior Learning

In this work we tackle the problem of estimating the density $f_X$ of a random variable $X$ by successive smoothing, such that the smoothed random variable $Y$ fulfills $(\partial_t - \Delta_1)f_Y(\,\cdot\,, t) = 0$, $f_Y(\,\cdot\,, 0) = f_X$. With a focus on image processing, we propose a product/fields of experts model with Gaussian mixture experts that admits an analytic expression for $f_Y (\,\cdot\,, t)$ under an orthogonality constraint on the filters. This construction naturally allows the model to be trained simultaneously over the entire diffusion horizon using empirical Bayes. We show preliminary results on image denoising where our model leads to competitive results while being tractable, interpretable, and having only a small number of learnable parameters. As a byproduct, our model can be used for reliable noise estimation, allowing blind denoising of images corrupted by heteroscedastic noise.

Explicit Diffusion of Gaussian Mixture Model Based Image Priors

Today Gadolinium-based contrast agents (GBCA) are indispensable in Magnetic Resonance Imaging (MRI) for diagnosing various diseases. However, GBCAs are expensive and may accumulate in patients with potential side effects, thus dose-reduction is recommended. Still, it is unclear to which extent the GBCA dose can be reduced while preserving the diagnostic value -- especially in pathological regions. To address this issue, we collected brain MRI scans at numerous non-standard GBCA dosages and developed a conditional GAN model for synthesizing corresponding images at fractional dose levels. Along with the adversarial loss, we advocate a novel content loss function based on the Wasserstein distance of locally paired patch statistics for the faithful preservation of noise. Our numerical experiments show that conditional GANs are suitable for generating images at different GBCA dose levels and can be used to augment datasets for virtual contrast models. Moreover, our model can be transferred to openly available datasets such as BraTS, where non-standard GBCA dosage images do not exist.

Erich Kobler

Papers

Learned Variational Video Color Propagation

Semi-supervised Brain Tumor Segmentation Using Diffusion Models

Blind Single Image Super-Resolution via Iterated Shared Prior Learning

Explicit Diffusion of Gaussian Mixture Model Based Image Priors

Faithful Synthesis of Low-dose Contrast-enhanced Brain MRI Scans using Noise-preserving Conditional GANs