SIAM Journal on Imaging Sciences, Volume 16, Issue 3, Page 1791-1824, September 2023.
Abstract. Parallel imaging (PI), relying on multicoils to sense [math]-space data, is an effective technique to accelerate magnetic resonance imaging by exploiting spatial sensitivity coding of multiple coils, with an integrated compressive sensing (CS) technology to achieve higher acceleration. In this paper, we propose a novel nonconvex reconstruction model and its proximal alternating linearized minimization (PALM) algorithm for PI in a blind setting that MR image and multichannel sensitivity maps are jointly estimated, regularized by image and sensitivity regularizers. Instead of hand-crafting the image and sensitivity regularizers, we propose unrolling the PALM algorithm to be a deep network for Blind Parallel MRI, dubbed as BPMRI-Net, with two learnable subnetworks to substitute the proximal operators of the image and sensitivity regularizers. We theoretically prove the linear convergence of BPMRI-Net as an iterative algorithm, which alternately updates two variables based on the learnable proximal operators. The learned BPMRI-Net can simultaneously output the MR image and sensitivity maps from undersampled multichannel [math]-space data even when the number of low-frequency sampling lines in the center of [math]-space is small. Numerical results demonstrate the effectiveness of our method with state-of-the-art reconstruction accuracy.

中文翻译：

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具有收敛保证的并行 MR 成像中联合图像和灵敏度估计的展开隐式正则化网络

SIAM 影像科学杂志，第 16 卷，第 3 期，第 1791-1824 页，2023 年 9 月。
抽象的。并行成像（PI）依靠多线圈来感测数学空间数据，是一种通过利用多个线圈的空间灵敏度编码来加速磁共振成像的有效技术，并结合集成压缩感测（CS）技术来实现更高的加速。在本文中，我们提出了一种新颖的非凸重建模型及其在盲设置下的PI的近端交替线性化最小化（PALM）算法，联合估计MR图像和多通道灵敏度图，并通过图像和灵敏度正则化器进行正则化。我们建议将 PALM 算法展开为盲并行 MRI 的深度网络，称为 BPMRI-Net，而不是手工制作图像和灵敏度正则化器，用两个可学习的子网络来替代图像和灵敏度正则化器的近端算子。我们从理论上证明了 BPMRI-Net 作为迭代算法的线性收敛性，该算法基于可学习的近端算子交替更新两个变量。即使[数学]空间中心的低频采样线数量很少，学习到的BPMRI-Net也可以同时从欠采样多通道[数学]空间数据输出MR图像和灵敏度图。数值结果证明了我们的方法的有效性和最先进的重建精度。即使[数学]空间中心的低频采样线数量很少，学习到的BPMRI-Net也可以同时从欠采样多通道[数学]空间数据输出MR图像和灵敏度图。数值结果证明了我们的方法的有效性和最先进的重建精度。即使[数学]空间中心的低频采样线数量很少，学习到的BPMRI-Net也可以同时从欠采样多通道[数学]空间数据输出MR图像和灵敏度图。数值结果证明了我们的方法的有效性和最先进的重建精度。