目的 快速成像一直是磁共振成像（MRI）技术中的焦点之一，现有多通道并行成像和部分k空间数据重建都是通过减少梯度编码步数来降低数据的获取时间，两者结合起来更能有效地提高扫描速度。然而，在欠采样倍数加高的情况下，依然有很严重的混叠伪影，因此研究一种在保证成像精度的前提下加快成像速度的方法尤为重要。方法 基于卷积神经网络的磁共振成像（CNN-MRI）方法利用大量现有的全采样多通道数据的先验信息，设计并线下训练一个深度卷积神经网络，学习待重建图像与全采样图像之间的映射关系，从而在线上成像时，欠采样所丢失数据能被训练好的网络进行预测。本文探讨了对于深度学习磁共振成像的可选择性欠采样方式，提出了一种新的欠采样轨迹方案。为了判断本文方法的性能，用峰值信噪比（PSNR）、结构相似度（SSIM）以及均方根差（RMSE）来作为衡量的指标。结果 实验结果表明，所提出欠采样方案的综合性能要优于传统欠采样轨迹，PSNR要高出12 dB，SSIM高出近0.1，RMSE要降低0.020.04左右。此外重建结果还与经典的并行重建方法GRAPPA（geneRalized autocalibrating partially parallel acquisitions）、SPIRiT（iterative self-consistent parallel imaging reconstruction from arbitrary k-space）以及SAKE（simultaneous autocalibrating and k-space estimation）作比较，从视觉效果以及各项量化指标得出本文方法能重建出更准确的结果，并且重建速度要快5倍以上。结论 深度学习方法能很好地在线下训练时从大量数据集中提取并学习到有价值的先验信息，所以在线上测试时能在较短时间内重建出优于经典算法的高质量结果；提出的1维低频汉明滤波欠采样方案则有利于提升该网络的性能。

Objective Magnetic resonance imaging (MRI) with non-ionizing and non-radiating nature is capable of providing rich anatomical and functional information and is an indispensable tool for medical diagnosis, disease staging, and clinical research.However, many advanced applications, such as cardiovascular imaging, magnetic resonance (MR) spectroscopy, and functional MRI, have not been widely used in clinical practice given the extended scanning time of MRI. Thus, fast imaging has been constantly one of the emphases in the MRI technology. The existing multi-coil parallel imaging and partial k-space data reconstruction techniques decrease acquisition times by reducing the amount of phase encoding required. The parallel imaging based on utilizing the spatial sensitivity of multiple coils with gradient encoding has been an essential technique for accelerating MRI scan. In addition to exploring the physical properties of multiple coils, an increasing number of researchers have been using signal processing in MR image reconstruction. Specifically, diverse prior information as regularizations is incorporated into the reconstruction equation inside. One of the representative efforts focuses on compressed sensing, which utilizes image sparsity and incoherent undersampling for fast MRI. The benefit of the combination compared with the individual techniques is the significantly increased scanning rate. However, serious aliasing artifacts may still occur in case of a high acceleration factor. Therefore, a means of accelerating the imaging rate while ensuring imaging accuracy should be devised. Method The wide application of convolutional neural network (CNN) has revealed its powerful capability incorrelation exploration, automatic feature extraction, and nonlinear correlation description. Therefore, we apply CNN to medical MR image reconstruction and design a multi-coil CNN to exploit the local correlation in multi-channel images. The proposed MRI based on the convolutional neural network (CNN-MRI) method utilizes prior knowledge from numerous existing fully-sampled multi-coil data. The proposed method designs and trains an off-line deep CNN to describe the mapping relationship between zero-filled and fully sampled MR images. The trained network is then used for the online prediction of images from the undersampled multi-channel data. The entire research contents include two main parts as follows:off-line training and online imaging. The two important components in the off-line training are the preprocessing of big datasets for training samples and the network design. We directly predict images online with the trained network parameter model in the online imaging. This paper discusses the undersampling methods for MRI based on deep learning. Unlike the popular parallel imaging or compressed sensing technique, which exploits sensitivity and sparsity for fast MRI, CNN-MRI learns the end-to-end mapping between the MR images reconstructed from the undersampled and fully-sampled k-space data from huge offline acquisitions, and then aids in exacting online fast imaging with the learned mapping prior. Therefore, conventional sampling methods may not be the optimal undersampling trajectory for CNN-MRI, in which uniform and incoherent undersampling are required for parallel and compressed sensing MRI, respectively. Furthermore, three 1D undersampling patterns, namely, 1D random undersampling with variable density, 1D uniform undersampling, and 1D low frequency, have been investigated with the proposed CNN-MRI framework.Specifically, we proposed a new trajectory scheme, namely, hamming filtered asymmetrical 1D partial Fourier sampling. The reconstruction results were quantitatively evaluated in terms of peak signal-to-noise ratio (PSNR), structural similarity (SSIM), and root-mean-square error (RMSE) to determine the performance of the proposed scheme. Result Experimental results show that the proposed undersampling pattern performs better than the traditional sampling trajectory. The PSNR improved by 1 dB to 2 dB, the SSIM ratio improved by approximately 0.1, and the RMSE decreased by approximately 0.020.04. In addition, we compared the proposed method to the classical parallel imaging methods, GRAPPA, SPIRiT, and SAKE, at an acceleration factor of 4. GRAPPA, SPIRiT, and SAKE has used their typical uniform undersampling patterns with autocalibration lines and parameter settings. For CNN-MRI, we adopted the hamming filtered 1D low-frequency trajectory, with a shifting distance of 18. For a quantitative comparison, four MRI images were tested with the different methods, which mean index values in PSNR, SSIM, and RMSE are summarized. The images reconstructed through the proposed method were closer to the ground truth image, while aliasing artifacts were observed in the images reconstructed using GRAPPA/SPIRiT/SAKE. The mean PSNR of the proposed method improved by 0.54 dB, the mean SSIM ratio improved by 0.150.27, and the mean RMSE decreased by approximately 0.010.07. Synthetically, the mean quantitative and visual comparisons show that the proposed method produces superior quality with the least time, with a reconstruction rate of faster than five times. Conclusion Deep learning can learn valuable prior knowledge from big off-line datasets, and then perform high-quality online image reconstruction from undersampled MR data with a low computational cost. The hamming filtered 1D low-frequency undersampling pattern was developed to improve the performance of the proposed CNN. Future work will further optimize the undersampling trajectories, which can also be extended to non-Cartesian sampling design, and include additional big data in the proposed framework to extract further valuable prior information for fast MRI.