You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
The goal of MRI reconstruction is to restore a high fidelity image from partially observed measurements. This partial view naturally induces reconstruction uncertainty that can only be reduced by acquiring additional measurements. In this paper, we present a novel method for MRI reconstruction that, at inference time, dynamically selects the measurements to take and iteratively refines the prediction in order to best reduce the reconstruction error and, thus, its uncertainty. We validate our method on a large scale knee MRI dataset, as well as on ImageNet. Results show that (1) our system successfully outperforms active acquisition baselines; (2) our uncertainty estimates correlate with error maps; and (3) our ResNet-based architecture surpasses standard pixel-to-pixel models in the task of MRI reconstruction. The proposed method not only shows high-quality reconstructions but also paves the road towards more applicable solutions for accelerating MRI.

Cited Abstract(s):
[1]: We investigate conditional adversarial networks as a general-purpose solution to image-to-image translation problems. These networks not only learn the mapping from input image to output image, but also learn a loss function to train this mapping. This makes it possible to apply the same generic approach to problems that traditionally would require very different loss formulations. We demonstrate that this approach is effective at synthesizing photos from label maps, reconstructing objects from edge maps, and colorizing images, among other tasks. Indeed, since the release of the pix2pix software associated with this paper, a large number of internet users (many of them artists) have posted their own experiments with our system, further demonstrating its wide applicability and ease of adoption without the need for parameter tweaking. As a community, we no longer hand-engineer our mapping functions, and this work suggests we can achieve reasonable results without hand-engineering our loss functions either.

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[8]: The sparsity which is implicit in MR images is exploited to significantly undersample k -space. Some MR images such as angiograms are already sparse in the pixel representation; other, more complicated images have a sparse representation in some transform domain–for example, in terms of spatial finite-differences or their wavelet coefficients. According to the recently developed mathematical theory of compressedsensing, images with a sparse representation can be recovered from randomly undersampled k -space data, provided an appropriate nonlinear recovery scheme is used. Intuitively, artifacts due to random undersampling add as noise-like interference. In the sparse transform domain the significant coefficients stand out above the interference. A nonlinear thresholding scheme can recover the sparse coefficients, effectively recovering the image itself. In this article, practical incoherent undersampling schemes are developed and analyzed by means of their aliasing interference. Incoherence is introduced by pseudo-random variable-density undersampling of phase-encodes. The reconstruction is performed by minimizing the 1 norm of a transformed image, subject to data

[9]: Inspired by recent advances in deep learning, we propose a framework for reconstructing dynamic sequences of 2-D cardiac magnetic resonance (MR) images from undersampled data using a deep cascade of convolutional neural networks (CNNs) to accelerate the data acquisition process. In particular, we address the case where data are acquired using aggressive Cartesian undersampling. First, we show that when each 2-D image frame is reconstructed independently, the proposed method outperforms state-of-the-art 2-D compressed sensing approaches, such as dictionary learning-based MR image reconstruction, in terms of reconstruction error and reconstruction speed. Second, when reconstructing the frames of the sequences jointly, we demonstrate that CNNs can learn spatio-temporal correlations efficiently by combining convolution and data sharing approaches. We show that the proposed method consistently outperforms state-of-the-art methods and is capable of preserving anatomical structure more faithfully up to 11-fold undersampling. Moreover, reconstruction is very fast: each complete dynamic sequence can be reconstructed in less than 10 s and, for the 2-D case, each image frame can be reconstructed in 23 ms, enabling real-time applications.

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[12]: Compressed sensing magnetic resonance imaging (CS-MRI) has provided theoretical foundations upon which the time-consuming MRI acquisition process can be accelerated. However, it primarily relies on iterative numerical solvers, which still hinders their adaptation in time-critical applications. In addition, recent advances in deep neural networks have shown their potential in computer vision and image processing, but their adaptation to MRI reconstruction is still in an early stage. In this paper, we propose a novel deep learning-based generative adversarial model, RefineGAN , for fast and accurate CS-MRI reconstruction. The proposed model is a variant of fully-residual convolutional autoencoder and generative adversarial networks (GANs), specifically designed for CS-MRI formulation; it employs deeper generator and discriminator networks with cyclic data consistency loss for faithful interpolation in the given under-sampled @math -space data. In addition, our solution leverages a chained network to further enhance the reconstruction quality. RefineGAN is fast and accurate—the reconstruction process is extremely rapid, as low as tens of milliseconds for reconstruction of a @math image, because it is one-way deployment on a feed-forward network, and the image quality is superior even for extremely low sampling rate (as low as 10 ) due to the data-driven nature of the method. We demonstrate that RefineGAN outperforms the state-of-the-art CS-MRI methods by a large margin in terms of both running time and image quality via evaluation using several open-source MRI databases.

[13]: This article reviews the requirements for successful compressed sensing (CS), describes their natural fit to MRI, and gives examples of four interesting applications of CS in MRI. The authors emphasize on an intuitive understanding of CS by describing the CS reconstruction as a process of interference cancellation. There is also an emphasis on the understanding of the driving factors in applications, including limitations imposed by MRI hardware, by the characteristics of different types of images, and by clinical concerns.

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[16]: Magnetic Resonance Imaging (MRI) typically collects data below the Nyquist sampling rate for imaging acceleration. To remove aliasing artifacts, we propose a multi-channel deep generative adversarial network (GAN) model for MRI reconstruction. Because multi-channel GAN matches the parallel data acquisition system architecture on a modern MRI scanner, this model can effectively learn intrinsic data correlation associated with MRI hardware from originally-collected multi-channel complex data. By estimating missing data directly with the trained network, images may be generated from undersampled multi-channel raw data, providing an “end-to-end” approach to parallel MRI reconstruction. By experimentally comparing with other methods, it is demonstrated that multi-channel GAN can perform image reconstruction with an affordable computation cost and an imaging acceleration factor higher than the current clinical standard.

[17]: Many fundamental image-related problems involve deconvolution operators. Real blur degradation seldom complies with an ideal linear convolution model due to camera noise, saturation, image compression, to name a few. Instead of perfectly modeling outliers, which is rather challenging from a generative model perspective, we develop a deep convolutional neural network to capture the characteristics of degradation. We note directly applying existing deep neural networks does not produce reasonable results. Our solution is to establish the connection between traditional optimization-based schemes and a neural network architecture where a novel, separable structure is introduced as a reliable support for robust deconvolution against artifacts. Our network contains two submodules, both trained in a supervised manner with proper initialization. They yield decent performance on non-blind image deconvolution compared to previous generative-model based methods.

[18]: There is large consent that successful training of deep networks requires many thousand annotated training samples. In this paper, we present a network and training strategy that relies on the strong use of data augmentation to use the available annotated samples more efficiently. The architecture consists of a contracting path to capture context and a symmetric expanding path that enables precise localization. We show that such a network can be trained end-to-end from very few images and outperforms the prior best method (a sliding-window convolutional network) on the ISBI challenge for segmentation of neuronal structures in electron microscopic stacks. Using the same network trained on transmitted light microscopy images (phase contrast and DIC) we won the ISBI cell tracking challenge 2015 in these categories by a large margin. Moreover, the network is fast. Segmentation of a 512x512 image takes less than a second on a recent GPU. The full implementation (based on Caffe) and the trained networks are available at this http URL .

[19]: Compressed sensing proposes to reconstruct more degrees of freedom in a signal than the number of values actually measured. Compressed sensing therefore risks introducing errors -- inserting spurious artifacts or masking the abnormalities that medical imaging seeks to discover. The present case study of estimating errors using the standard statistical tools of a jackknife and a bootstrap yields error "bars" in the form of full images that are remarkably representative of the actual errors (at least when evaluated and validated on data sets for which the ground truth and hence the actual error is available). These images show the structure of possible errors -- without recourse to measuring the entire ground truth directly -- and build confidence in regions of the images where the estimated errors are small.
There is a vast literature tackling the problem of undersampled MRI reconstruction. State-of-the-art solutions include both signal processing techniques (e.g. Compressed Sensing (CS)) as well as machine learning ones. On one hand, CS-based MRI reconstruction has been widely studied in the literature [4]7 [6] [8] [12] [19] . These approaches usually result in over-smoothed reconstructions, which involve a time consuming optimization process, limiting their practical scalability. On other hand, deep learning based approaches have been introduced as a promising alternative to MRI reconstruction [4]4 [15] [4] [3] [2] . In [4]3 , a cascaded CNN with a consistency layer is presented to ensure measurement fidelity in dynamic cardiac MRI reconstruction. In [10] , a Unet architecture [18] is used to reconstruct brain images, while [7] proposes a recurrent inference machine for image reconstruction. Moreover, following recent trends, architectures involving image refinement mechanisms seem to be gaining increasing attention [4]3 [3]2 [7] . Although all previously-mentioned approaches are able to improve the reconstruction error, the human perception of the results is still not compelling. Therefore, recent works have also focused on exploring different training objectives such as adversarial losses [4]5 [4]0 [1] to enhance the perceptual reconstruction quality [3]2 [16] .