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The application of compressed sensing (CS)-enabled data reconstruction for accelerating magnetic resonance imaging (MRI) remains a challenging problem. This is due to the fact that the information lost in k-space from the acceleration mask makes it difficult to reconstruct an image similar to the quality of a fully sampled image. Multiple deep learning-based structures have been proposed for MRI reconstruction using CS, in both the k-space and image domains, and using unrolled optimization methods. However, the drawback of these structures is that they are not fully utilizing the information from both domains (k-space and image). Herein, we propose a deep learning-based attention hybrid variational network that performs learning in both the k-space and image domains. We evaluate our method on a well-known open-source MRI dataset (652 brain cases and 1172 knee cases) and a clinical MRI dataset of 243 patients diagnosed with strokes from our institution to demonstrate the performance of our network. Our model achieves an overall peak signal-to-noise ratio/structural similarity of 40.92 ± 0.29/0.9577 ± 0.0025 (fourfold) and 37.03 ± 0.25/0.9365 ± 0.0029 (eightfold) for the brain dataset, 31.09 ± 0.25/0.6901 ± 0.0094 (fourfold) and 29.49 ± 0.22/0.6197 ± 0.0106 (eightfold) for the knee dataset, and 36.32 ± 0.16/0.9199 ± 0.0029 (20-fold) and 33.70 ± 0.15/0.8882 ± 0.0035 (30-fold) for the stroke dataset. In addition to quantitative evaluation, we undertook a blinded comparison of image quality across networks performed by a subspecialty trained radiologist. Overall, we demonstrate that our network achieves a superior performance among others under multiple reconstruction tasks. 

Abstract Global agricultural trade creates multiple telecoupled flows of nitrogen (N) and phosphorus (P). The flows of physical and virtual nutrients along with trade have discrepant effects on natural resources in different countries. However, existing literature has not quantified or analyzed such effects yet. Here we quantified the physical and virtual N and P flows embedded in the global agricultural trade networks from 1997 to 2016 and elaborated components of the telecoupling framework. The N and P flows both increased continuously and more than 25% of global consumption of nutrients in agricultural products were related to physical nutrient flows, while virtual nutrient flows were equivalent to one-third of the nutrients inputs into global agricultural system. These flows have positive telecoupling effects on saving N and P resources at the global scale. Reducing inefficient trade flows will enhance resource conservation, environmental sustainability in the hyper-globalized world.