Undersampled magnetic resonance image (MRI) reconstruction is typically an ill-posed linear inverse task. The time and resource intensive computations require trade offs between accuracy and speed. In addition, state-of-the-art compressed sensing (CS) analytics are not cognizant of the image diagnostic quality. To address these challenges, we propose a novel CS framework that uses generative adversarial networks (GAN) to model the (low-dimensional) manifold of high-quality MR images. Leveraging a mixture of least-squares (LS) GANs and pixel-wise ℓ1/ℓ2 cost, a deep residual network with skip connections is trained as the generator that learns to remove the aliasing artifacts by projecting onto the image manifold. The LSGAN learns the texture details, while the ℓ1/ℓ2 cost suppresses high-frequency noise. A discriminator network, which is a multilayer convolutional neural network (CNN), plays the role of a perceptual cost that is then jointly trained based on high quality MR images to score the quality of retrieved images. In the operational phase, an initial aliased estimate (e.g., simply obtained by zero-filling) is propagated into the trained generator to output the desired reconstruction. This demands very low computational overhead. Extensive evaluations are performed on a large contrast-enhanced MR dataset of pediatric patients. Images rated by expert radiologists corroborate that GANCS retrieves higher quality images with improved fine texture details compared with conventional Wavelet-based and dictionary-learning based CS schemes as well as with deeplearning based schemes using pixel-wise training. In addition, it offers reconstruction times of under a few milliseconds, which is two orders of magnitude faster than current state-of-the-art CS-MRI schemes.

Extracting latent low-dimensional structure from high-dimensional data is of paramount importance in timely inference tasks encountered with 'Big Data' analytics. However, increasingly noisy, heterogeneous, and incomplete datasets as well as the need for real-time processing of streaming data pose major challenges to this end. In this context, the present paper permeates benefits from rank minimization to scalable imputation of missing data, via tracking low-dimensional subspaces and unraveling latent (possibly multi-way) structure from incomplete streaming data. For low-rank matrix data, a subspace estimator is proposed based on an exponentially-weighted least-squares criterion regularized with the nuclear norm. After recasting the non-separable nuclear norm into a form amenable to online optimization, real-time algorithms with complementary strengths are developed and their convergence is established under simplifying technical assumptions. In a stationary setting, the asymptotic estimates obtained offer the well-documented performance guarantees of the batch nuclear-norm regularized estimator. Under the same unifying framework, a novel online (adaptive) algorithm is developed to obtain multi-way decompositions of low-rank tensors with missing entries, and perform imputation as a byproduct. Simulated tests with both synthetic as well as real Internet and cardiac magnetic resonance imagery (MRI) data confirm the efficacy of the proposed algorithms, and their superior performance relative to state-of-the-art alternatives.

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FourCastNet, short for Fourier ForeCasting Neural Network, is a global data-driven weather forecasting model that provides accurate short to medium-range global predictions at 0.25 • resolution. FourCastNet accurately forecasts high-resolution, fast-timescale variables such as the surface wind speed, precipitation, and atmospheric water vapor. It has important implications for planning wind energy resources, predicting extreme weather events such as tropical cyclones, extra-tropical cyclones, and atmospheric rivers. FourCastNet matches the forecasting accuracy of the ECMWF Integrated Forecasting System (IFS), a state-of-the-art Numerical Weather Prediction (NWP) model, at short lead times for large-scale variables, while outperforming IFS for small-scale variables, including precipitation. FourCastNet generates a week-long forecast in less than 2 seconds, orders of magnitude faster than IFS. The speed of FourCastNet enables the creation of rapid and inexpensive large-ensemble forecasts with thousands of ensemble-members for improving probabilistic forecasting. We discuss how data-driven deep learning models such as FourCastNet are a valuable addition to the meteorology toolkit to aid and augment NWP models.

Compressed sensing (CS) reconstruction methods leverage sparse structure in underlying signals to recover high-resolution images from highly undersampled measurements. When applied to magnetic resonance imaging (MRI), CS has the potential to dramatically shorten MRI scan times, increase diagnostic value, and improve overall patient experience. However, CS has several shortcomings which limit its clinical translation such as: 1) artifacts arising from inaccurate sparse modelling assumptions, 2) extensive parameter tuning required for each clinical application, and 3) clinically infeasible reconstruction times. Recently, CS has been extended to incorporate deep neural networks as a way of learning complex image priors from historical exam data. Commonly referred to as unrolled neural networks, these techniques have proven to be a compelling and practical approach to address the challenges of sparse CS. In this tutorial, we will review the classical compressed sensing formulation and outline steps needed to transform this formulation into a deep learning-based reconstruction framework. Supplementary open source code in Python will be used to demonstrate this approach with open databases. Further, we will discuss considerations in applying unrolled neural networks in the clinical setting.

Given the superposition of a low-rank matrix plus the product of a known fat compression matrix times a sparse matrix, the goal of this paper is to establish deterministic conditions under which exact recovery of the low-rank and sparse components becomes possible. This fundamental identifiability issue arises with traffic anomaly detection in backbone networks, and subsumes compressed sensing as well as the timely low-rank plus sparse matrix recovery tasks encountered in matrix decomposition problems.Leveraging the ability of ℓ 1 -and nuclear norms to recover sparse and low-rank matrices, a convex program is formulated to estimate the unknowns. Analysis and simulations confirm that the said convex program can recover the unknowns for sufficiently low-rank and sparse enough components, along with a compression matrix possessing an isometry property when restricted to operate on sparse vectors. When the low-rank, sparse, and compression matrices are drawn from certain random ensembles, it is established that exact recovery is possible with high probability. First-order algorithms are developed to solve the nonsmooth convex optimization problem with provable iteration complexity guarantees. Insightful tests with synthetic and real network data corroborate the effectiveness of the novel approach in unveiling traffic anomalies across flows and time, and its ability to outperform existing alternatives.

Given a limited number of entries from the superposition of a low-rank matrix plus the product of a known fat compression matrix times a sparse matrix, recovery of the low-rank and sparse components is a fundamental task subsuming compressed sensing, matrix completion, and principal components pursuit. This paper develops algorithms for distributed sparsity-regularized rank minimization over networks, when the nuclear-and ℓ 1 -norm are used as surrogates to the rank and nonzero entry counts of the sought matrices, respectively. While nuclear-norm minimization has well-documented merits when centralized processing is viable, non-separability of the singular-value sum challenges its distributed minimization.To overcome this limitation, an alternative characterization of the nuclear norm is adopted which leads to a separable, yet non-convex cost minimized via the alternating-direction method of multipliers. The novel distributed iterations entail reduced-complexity per-node tasks, and affordable message passing among single-hop neighbors. Interestingly, upon convergence the distributed (non-convex) estimator provably attains the global optimum of its centralized counterpart, regardless of initialization. Several application domains are outlined to highlight the generality and impact of the proposed framework. These include unveiling traffic anomalies in backbone networks, predicting networkwide path latencies, and mapping the RF ambiance using wireless cognitive radios. Simulations with synthetic and real network data corroborate the convergence of the novel distributed algorithm, and its centralized performance guarantees.

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