IEEE Trans Med Imaging. 2014 Mar;33(3):668-81. doi: 10.1109/TMI.2013.2293974.
Recent theoretical results on low-rank matrix reconstruction have inspired significant interest in low-rank modeling of MRI images. Existing approaches have focused on higher-dimensional scenarios with data available from multiple channels, timepoints, or image contrasts. The present work demonstrates that single-channel, single-contrast, single-timepoint k-space data can also be mapped to low-rank matrices when the image has limited spatial support or slowly varying phase. Based on this, we develop a novel and flexible framework for constrained image reconstruction that uses low-rank matrix modeling of local k-space neighborhoods (LORAKS). A new regularization penalty and corresponding algorithm for promoting low-rank are also introduced. The potential of LORAKS is demonstrated with simulated and experimental data for a range of denoising and sparse-sampling applications. LORAKS is also compared against state-of-the-art methods like homodyne reconstruction, l1-norm minimization, and total variation minimization, and is demonstrated to have distinct features and advantages. In addition, while calibration-based support and phase constraints are commonly used in existing methods, the LORAKS framework enables calibrationless use of these constraints.
近期关于低秩矩阵重构的理论成果激发了人们对 MRI 图像的低秩建模的极大兴趣。现有的方法主要集中在具有多通道、多个时间点或图像对比数据的高维场景中。本研究表明，当图像的空间支持度有限或相位变化缓慢时，单通道、单对比度、单时间点的 k 空间数据也可以映射到低秩矩阵中。基于此，我们开发了一种新颖而灵活的约束图像重建框架，该框架使用局部 k 空间邻域（LORAKS）的低秩矩阵建模。同时，还引入了一种新的正则化惩罚项和相应的算法来促进低秩。通过对一系列去噪和稀疏采样应用的模拟和实验数据，展示了 LORAKS 的潜力。还将 LORAKS 与同态重建、l1 范数最小化和全变差最小化等最先进的方法进行了比较，结果表明 LORAKS 具有独特的特征和优势。此外，虽然现有的方法通常使用基于校准的支撑和相位约束，但 LORAKS 框架可以实现这些约束的无校准使用。
