Yiasemis George, Moriakov Nikita, Sonke Jan-Jakob, Teuwen Jonas
Department of Radiation Oncology, the Netherlands Cancer Institute, Plesmanlaan 121, Amsterdam 1066 CX, the Netherlands; University of Amsterdam, Science Park 904, Amsterdam 1098 XH, the Netherlands.
Department of Radiation Oncology, the Netherlands Cancer Institute, Plesmanlaan 121, Amsterdam 1066 CX, the Netherlands; University of Amsterdam, Science Park 904, Amsterdam 1098 XH, the Netherlands; Department of Medical Imaging, Radboud University Medical Center, Geert Grooteplein Zuid 10, Nijmegen 6525 GA, the Netherlands.
Magn Reson Imaging. 2025 Jan;115:110266. doi: 10.1016/j.mri.2024.110266. Epub 2024 Oct 24.
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.
医学成像（MI）任务，如加速并行磁共振成像（MRI），通常涉及从噪声或不完整测量中重建图像。这相当于解决不适定逆问题，而这种问题没有令人满意的闭式解析解。MRI重建中的传统方法，如压缩感知（CS），可能耗时或容易得到低保真图像。最近，大量深度学习（DL）方法在解决逆问题方面表现出卓越性能，超越了传统方法。在本研究中，我们提出了vSHARP（用于逆问题重建的可变分裂半二次交替方向乘子法），这是一种基于深度学习的新颖方法，用于解决医学成像中出现的不适定逆问题。vSHARP利用半二次可变分裂方法，并采用交替方向乘子法（ADMM）展开优化过程。为了保证数据一致性，vSHARP在图像域展开一个可微梯度下降过程，同时应用基于深度学习的去噪器，如U-Net架构，来提高图像质量。vSHARP还采用基于扩张卷积深度学习的模型来预测ADMM初始化的拉格朗日乘子。我们使用两个不同的数据集对vSHARP进行加速并行MRI重建任务评估，并使用另一个数据集对其进行加速并行动态MRI重建评估。我们与现有最先进方法的对比分析表明，vSHARP在这些应用中具有卓越性能。
