论文标题
结合频带限制的参数化和半拉格朗日朗格 - kutta集成，以实现有效的PDE限制的LDDMM
Combining the band-limited parameterization and Semi-Lagrangian Runge--Kutta integration for efficient PDE-constrained LDDMM
论文作者
论文摘要
PDE受限的LDDMM方法家族正在成为一种特别有趣的方法，用于物理有意义的差异转化。高斯（Newton-Newton-krylov优化和runge）的原始组合 - kutta集成显示出极好的数值准确性和快速收敛速度。但是，其最重要的限制是巨大的计算复杂性，阻碍了其在计算解剖学应用研究中的广泛使用。该限制已通过带限制矢量场和半拉格朗日集成的空间中的问题表述独立处理。这项工作的目的是将两者结合在带限制的PDE限制的LDDMM的三种变体中，以进一步提高其计算效率。广泛评估所得方法的准确性。对于所有变体，提出的组合方法都显示出计算效率的显着增长。此外，就准确性和效率而言，基于变形状态方程的变体始终定位为所有评估框架的最佳性能方法。
The family of PDE-constrained LDDMM methods is emerging as a particularly interesting approach for physically meaningful diffeomorphic transformations. The original combination of Gauss--Newton--Krylov optimization and Runge--Kutta integration, shows excellent numerical accuracy and fast convergence rate. However, its most significant limitation is the huge computational complexity, hindering its extensive use in Computational Anatomy applied studies. This limitation has been treated independently by the problem formulation in the space of band-limited vector fields and Semi-Lagrangian integration. The purpose of this work is to combine both in three variants of band-limited PDE-constrained LDDMM for further increasing their computational efficiency. The accuracy of the resulting methods is evaluated extensively. For all the variants, the proposed combined approach shows a significant increment of the computational efficiency. In addition, the variant based on the deformation state equation is positioned consistently as the best performing method across all the evaluation frameworks in terms of accuracy and efficiency.
