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As a follow-up to the first IEEE Transactions on Medical Imaging (TMI) special issue on the theme of deep tomographic reconstruction, the second special issue is assembled to reflect the status and momentum of this rapidly emerging field. In this editorial, we provide a brief background illustrating the motivation for the development of network-based, data-driven, and learning-oriented reconstruction methods, summarize the included papers, and report our verification of the shared deep learning codes. Finally, we discuss several important research topics to facilitate further investigation and collaboration. [ABSTRACT FROM AUTHOR]

We introduce a model-based deep learning architecture termed MoDL-MUSSELS for the correction of phase errors in multishot diffusion-weighted echo-planar MR images. The proposed algorithm is a generalization of the existing MUSSELS algorithm with similar performance but significantly reduced computational complexity. In this work, we show that an iterative re-weighted least-squares implementation of MUSSELS alternates between a multichannel filter bank and the enforcement of data consistency. The multichannel filter bank projects the data to the signal subspace, thus exploiting the annihilation relations between shots. Due to the high computational complexity of the self-learned filter bank, we propose replacing it with a convolutional neural network (CNN) whose parameters are learned from exemplary data. The proposed CNN is a hybrid model involving a multichannel CNN in the k-space and another CNN in the image space. The k-space CNN exploits the annihilation relations between the shot images, while the image domain network is used to project the data to an image manifold. The experiments show that the proposed scheme can yield reconstructions that are comparable to state-of-the-art methods while offering several orders of magnitude reduction in run-time. [ABSTRACT FROM AUTHOR]

We introduce a model-based image reconstruction framework with a convolution neural network (CNN)-based regularization prior. The proposed formulation provides a systematic approach for deriving deep architectures for inverse problems with the arbitrary structure. Since the forward model is explicitly accounted for, a smaller network with fewer parameters is sufficient to capture the image information compared to direct inversion approaches. Thus, reducing the demand for training data and training time. Since we rely on end-to-end training with weight sharing across iterations, the CNN weights are customized to the forward model, thus offering improved performance over approaches that rely on pre-trained denoisers. Our experiments show that the decoupling of the number of iterations from the network complexity offered by this approach provides benefits, including lower demand for training data, reduced risk of overfitting, and implementations with significantly reduced memory footprint. We propose to enforce data-consistency by using numerical optimization blocks, such as conjugate gradients algorithm within the network. This approach offers faster convergence per iteration, compared to methods that rely on proximal gradients steps to enforce data consistency. Our experiments show that the faster convergence translates to improved performance, primarily when the available GPU memory restricts the number of iterations. [ABSTRACT FROM AUTHOR]

Current deep learning-based manifold learning algorithms such as the variational autoencoder (VAE) require fully sampled data to learn the probability density of real-world datasets. However, fully sampled data is often unavailable in a variety of problems, including the recovery of dynamic and high-resolution magnetic resonance imaging (MRI). We introduce a novel variational approach to learn a manifold from undersampled data. The VAE uses a decoder fed by latent vectors, drawn from a conditional density estimated from the fully sampled images using an encoder. Since fully sampled images are not available in our setting, we approximate the conditional density of the latent vectors by a parametric model whose parameters are estimated from the undersampled measurements using back-propagation. We use the framework for the joint alignment and recovery of multi-slice free breathing and ungated cardiac MRI data from highly undersampled measurements. Experimental results demonstrate the utility of the proposed scheme in dynamic imaging alignment and reconstructions. [ABSTRACT FROM AUTHOR]

Bilinear models such as low-rank and dictionary methods, which decompose dynamic data to spatial and temporal factor matrices are powerful and memory-efficient tools for the recovery of dynamic MRI data. Current bilinear methods rely on sparsity and energy compaction priors on the factor matrices to regularize the recovery. Motivated by deep image prior, we introduce a novel bilinear model, whose factor matrices are generated using convolutional neural networks (CNNs). The CNN parameters, and equivalently the factors, are learned from the undersampled data of the specific subject. Unlike current unrolled deep learning methods that require the storage of all the time frames in the dataset, the proposed approach only requires the storage of the factors or compressed representation; this approach allows the direct use of this scheme to large-scale dynamic applications, including free breathing cardiac MRI considered in this work. To reduce the run time and to improve performance, we initialize the CNN parameters using existing factor methods. We use sparsity regularization of the network parameters to minimize the overfitting of the network to measurement noise. Our experiments on free-breathing and ungated cardiac cine data acquired using a navigated golden-angle gradient-echo radial sequence show the ability of our method to provide reduced spatial blurring as compared to classical bilinear methods as well as a recent unsupervised deep-learning approach. [ABSTRACT FROM AUTHOR]