Medical Imaging (MI) tasks, such as accelerated parallel Magnetic Resonance Imaging (MRI), often involve reconstructing an image from noisy or incomplete measurements. This amounts to solving ill-posed inverse problems, where a satisfactory closed-form analytical solution is not available. Traditional methods such as Compressed Sensing (CS) in MRI reconstruction can be time-consuming or prone to obtaining low-fidelity images. Recently, a plethora of Deep Learning (DL) approaches have demonstrated superior performance in inverse-problem solving, surpassing conventional methods. In this study, we propose vSHARP (variable Splitting Half-quadratic ADMM algorithm for Reconstruction of inverse Problems), a novel DL-based method for solving ill-posed inverse problems arising in MI. vSHARP utilizes the Half-Quadratic Variable Splitting method and employs the Alternating Direction Method of Multipliers (ADMM) to unroll the optimization process. For data consistency, vSHARP unrolls a differentiable gradient descent process in the image domain, while a DL-based denoiser, such as a U-Net architecture, is applied to enhance image quality. vSHARP also employs a dilated-convolution DL-based model to predict the Lagrange multipliers for the ADMM initialization. We evaluate vSHARP on tasks of accelerated parallel MRI Reconstruction using two distinct datasets and on accelerated parallel dynamic MRI Reconstruction using another dataset. Our comparative analysis with state-of-the-art methods demonstrates the superior performance of vSHARP in these applications.

翻译：医学成像（MI）任务，例如加速并行磁共振成像（MRI），通常涉及从噪声或不完整的测量数据中重建图像。这相当于求解不适定的反问题，而此类问题通常无法获得令人满意的闭式解析解。传统方法（如MRI重建中的压缩感知（CS））可能耗时较长或易获得低保真度图像。近年来，大量深度学习（DL）方法在反问题求解中展现出超越传统方法的优越性能。在本研究中，我们提出了vSHARP（用于反问题重建的可变分裂半二次ADMM算法），这是一种新颖的基于深度学习的方法，用于求解MI中出现的不适定反问题。vSHARP利用半二次变量分裂方法，并采用乘子交替方向法（ADMM）来展开优化过程。为保持数据一致性，vSHARP在图像域展开了一个可微分的梯度下降过程，同时应用基于深度学习的去噪器（如U-Net架构）来提升图像质量。vSHARP还采用了一个基于扩张卷积的深度学习模型来预测ADMM初始化的拉格朗日乘子。我们使用两个不同的数据集在加速并行MRI重建任务上，以及使用另一个数据集在加速并行动态MRI重建任务上评估了vSHARP。与最先进方法的对比分析表明，vSHARP在这些应用中具有卓越的性能。