Goal: This work aims at developing a novel calibration-free fast parallel MRI (pMRI) reconstruction method incorporate with discrete-time optimal control framework. The reconstruction model is designed to learn a regularization that combines channels and extracts features by leveraging the information sharing among channels of multi-coil images. We propose to recover both magnitude and phase information by taking advantage of structured convolutional networks in image and Fourier spaces. Methods: We develop a novel variational model with a learnable objective function that integrates an adaptive multi-coil image combination operator and effective image regularization in the image and Fourier spaces. We cast the reconstruction network as a structured discrete-time optimal control system, resulting in an optimal control formulation of parameter training where the parameters of the objective function play the role of control variables. We demonstrate that the Lagrangian method for solving the control problem is equivalent to back-propagation, ensuring the local convergence of the training algorithm. Results: We conduct a large number of numerical experiments of the proposed method with comparisons to several state-of-the-art pMRI reconstruction networks on real pMRI datasets. The numerical results demonstrate the promising performance of the proposed method evidently. Conclusion: We conduct a large number of numerical experiments of the proposed method with comparisons to several state-of-the-art pMRI reconstruction networks on real pMRI datasets. The numerical results demonstrate the promising performance of the proposed method evidently. Significance: By learning multi-coil image combination operator and performing regularizations in both image domain and k-space domain, the proposed method achieves a highly efficient image reconstruction network for pMRI.
翻译:目标: 这项工作旨在开发一个新的无校准的快速平行MRI(pMRI)重建方法,该方法与离散时间的最佳控制框架相结合。重建模型旨在学习一种正规化方法,将通道和提取特征结合起来,利用多岩层图像渠道之间的信息共享。我们提议利用图像和Fourier空间结构化的变异网络,恢复规模和阶段信息。方法:我们开发了一个新颖的变异模型,其可学习的客观功能将适应性多岩层图像组合操作器和图像和Freier空间的有效域域图像正规化结合起来。我们将重建网络作为一个结构化离散时间的最佳控制系统,从而形成一种参数培训的最佳控制配置,使目标功能参数的参数发挥控制变量变量变量的作用。我们提议利用图像和Freyer空间结构结构结构结构结构结构的变异变异网络来恢复规模和阶段信息。我们为图像和Freyeroral图像组合的组合组合进行了大量数字实验,在真实的PMRI数据集中,数字结果展示了高清晰的模型,在真实的模型中进行高额模型化的模型的模型。