Efficient, Convergent SENSE MRI Reconstruction for Nonperiodic Boundary Conditions via Tridiagonal Solvers.
Efficient, Convergent SENSE MRI Reconstruction for Nonperiodic Boundary Conditions via Tridiagonal Solvers.
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DOI：
10.1109/tci.2016.2626999
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发表时间：
2017-03
影响因子：
5.4
通讯作者：
Fessler JA
中科院分区：
文献类型：
--
作者：
Le M;Fessler JA
欠采样是减少MRI扫描采集时间的有效方法。加速MRI的策略，如并行MRI和压缩感知MRI，具有不可微的成本函数和计算要求高的操作，具有挑战性的图像重建问题。变量分割（VS）可以简化实现困难的图像重建问题，如并行MRI和压缩感知的结合，CS-SENSE-MRI。结合增广拉格朗日（AL）和交替最小化策略，变量分裂可以产生具有更简单辅助变量更新的迭代最小化算法。然而，任意变量分裂方案不能保证收敛。许多变量分裂策略与周期边界条件相结合。由此产生的循环Hessians能够进行<s:1> (n log n)计算，但可能会损害图像在空间边界的精度。我们提出了两种CS-SENSE-MRI方法，它们使用正则化和非周期边界条件来防止缠绕伪影。每个算法使用可并行的三对角线求解器在<s:1> (n)时间内有效地计算一个结果变量更新。AL-tridiag是一种VS方法，旨在实现非周期边界条件的高效计算。另一种被提出的算法，ADMM-tridiag，使用类似的VS方案，但也确保收敛到使用乘法器的交替方向方法（ADMM）所提出的代价函数的最小值。AL-tridiag和ADMM-tridiag的速度与先前的VS CS-SENSE-MRI重建算法AL-P2相当。我们还将三对角线VS方法应用于一个简单的图像绘制问题。
Undersampling is an effective method for reducing scan acquisition time for MRI. Strategies for accelerated MRI such as parallel MRI and Compressed Sensing MRI present challenging image reconstruction problems with non-differentiable cost functions and computationally demanding operations. Variable splitting (VS) can simplify implementation of difficult image reconstruction problems, such as the combination of parallel MRI and Compressed Sensing, CS-SENSE-MRI. Combined with augmented Lagrangian (AL) and alternating minimization strategies, variable splitting can yield iterative minimization algorithms with simpler auxiliary variable updates. However, arbitrary variable splitting schemes are not guaranteed to converge. Many variable splitting strategies are combined with periodic boundary conditions. The resultant circulant Hessians enable 𝒪(n log n) computation but may compromise image accuracy at the spatial boundaries. We propose two methods for CS-SENSE-MRI that use regularization with non-periodic boundary conditions to prevent wrap-around artifacts. Each algorithm computes one of the resulting variable updates efficiently in 𝒪(n) time using a parallelizable tridiagonal solver. AL-tridiag is a VS method designed to enable efficient computation for non-periodic boundary conditions. Another proposed algorithm, ADMM-tridiag, uses a similar VS scheme but also ensures convergence to a minimizer of the proposed cost function using the Alternating Direction Method of Multipliers (ADMM). AL-tridiag and ADMM-tridiag show speeds competitive with previous VS CS-SENSE-MRI reconstruction algorithm AL-P2. We also apply the tridiagonal VS approach to a simple image inpainting problem.