The denoising of Lagrangian trajectories based on regularized B-spline is investigated. The aim is to find systematic criteria for optimization of algorithms used in 4D-PTV in order to optimize the quality of 4D-PTV measurements of turbulent flows as well as high-order of turbulence statistics. We introduce and adapt to this context two innovative tuning strategies which are commonly used in the Tikhonov regularization of inverse problems based on $\mathcal{L}$-curve shape and Normalized Cumulative Periodogram (NCP). The corresponding strategies are tested on synthetic Lagrangian trajectories computed from Direct Numerical Simulation with additional white Gaussian noise. Error-based quantities like Signal-to-Noise Ratio as well as statistical Lagrangian quantities are investigated to compare the different strategies. We then apply the algorithm to experimental data from a 4D-PTV Lagrangian measurements in a turbulent Von Kármán flow. We show the ability of those strategies to optimize the quality of the signal compared to conventional methods. Moreover, the strategies are more adaptable to real experimental noise.

研究了基于正则化B样条的拉格朗日轨迹的去噪。目的是找到优化用于4D-PTV的算法的系统标准，以优化湍流的4D-PTV测量质量以及湍流统计的高阶。我们介绍了两种创新的调整策略并将其适应于这种情况，这些策略通常在基于Tikhonov的反问题正则化中基于$\mathcal{大号}$曲线形状和归一化累积周期图（NCP）。相应的策略在由直接数值模拟计算的合成拉格朗日轨迹上进行了测试，并带有额外的高斯白噪声。研究了基于误差的量（如信噪比）以及统计拉格朗日量，以比较不同的策略。然后，我们将该算法应用于来自湍流VonKármán流中4D-PTV拉格朗日测量的实验数据。与传统方法相比，我们展示了这些策略优化信号质量的能力。此外，这些策略更适合实际的实验噪声。