Magnetic field inhomogeneity estimation is important in some types of magnetic resonance imaging (MRI), including field-corrected reconstruction for fast MRI with long readout times, and chemical shift based water-fat imaging. Regularized field map estimation methods that account for phase wrapping and noise involve nonconvex cost functions that require iterative algorithms. Most existing minimization techniques were computationally or memory intensive for 3D datasets, and are designed for single-coil MRI. This article considers 3D MRI with optional consideration of coil sensitivity, and addresses the multi-echo field map estimation and water-fat imaging problem. Our efficient algorithm uses a preconditioned nonlinear conjugate gradient method based on an incomplete Cholesky factorization of the Hessian of the cost function, along with a monotonic line search. Numerical experiments show the computational advantage of the proposed algorithm over state-of-the-art methods with similar memory requirements.

中文翻译：

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3D MRI 中的高效正则化场图估计

磁场不均匀性估计在某些类型的磁共振成像 (MRI) 中很重要，包括用于读取时间长的快速 MRI 的场校正重建和基于化学位移的水脂成像。考虑相位缠绕和噪声的正则化场图估计方法涉及需要迭代算法的非凸成本函数。大多数现有的最小化技术对于 3D 数据集来说都是计算密集型或内存密集型的，并且是为单线圈 MRI 设计的。本文考虑了 3D MRI，可选择考虑线圈灵敏度，并解决多回波场图估计和水脂成像问题。我们的高效算法使用基于成本函数 Hessian 的不完全 Cholesky 分解的预处理非线性共轭梯度方法，以及单调线搜索。数值实验表明，与具有类似内存要求的最新方法相比，所提出的算法具有计算优势。