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 supervised and self-supervised 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 the proposed model by applying it to the task of accelerated Parallel MRI Reconstruction on two distinct datasets. We present a comparative analysis of our experimental results with state-of-the-art approaches, highlighting the superior performance of vSHARP.

翻译：摘要：医学成像任务，如加速并行磁共振成像，常常需要从含噪或不完整测量值中重构图像。这本质上是求解不适定反问题，此类问题无法获得满意的闭式解析解。传统方法（如压缩感知在MRI重构中的应用）可能耗时或易产生低保真图像。近年来，大量基于有监督和自监督的深度学习方法在求解反问题中展现出超越传统方法的卓越性能。本研究提出vSHARP（变量分裂半二次型ADMM反问题重构算法）——一种基于深度学习的新方法，用于解决医学成像中出现的非适定反问题。vSHARP采用半二次变量分裂方法，并利用交替方向乘子法（ADMM）展开优化过程。在数据一致性方面，vSHARP在图像域中展开可微梯度下降过程，同时采用基于深度学习的去噪器（如U-Net架构）提升图像质量。此外，vSHARP使用基于扩张卷积的深度学习模型预测ADMM初始化所需的拉格朗日乘子。我们通过将所提模型应用于两个不同数据集的加速并行MRI重构任务进行评估，并将实验结果与前沿方法进行对比分析，凸显vSHARP的优越性能。