Numerous fields of nonlinear physics, very different in nature, produce signals and images that share the common feature of being essentially constituted of piecewise homogeneous phases. Analyzing signals and images from corresponding experiments to construct relevant physical interpretations thus often requires detecting such phases and estimating accurately their characteristics (borders, feature differences, …). However, situations of physical relevance often comes with low to very low signal-to-noise ratio precluding the standard use of classical linear filtering for analysis and denoising and thus calling for the design of advanced nonlinear signal/image filtering techniques. Additionally, when dealing with experimental physics signals/images, a second limitation is the large amount of data that need to be analyzed to yield accurate and relevant conclusions requiring the design of fast algorithms. The present work proposes a unified signal/image nonlinear filtering procedure, with fast algorithms and a data-driven automated hyperparameter tuning, based on proximal algorithms and Stein unbiased estimator principles. The interest and potential of these tools are illustrated at work on low-confinement solid friction signals and porous media multiphase flows.

本质上非常不同的许多非线性物理学领域产生的信号和图像具有共同的特征，即基本上由分段均质相组成。因此，分析来自相应实验的信号和图像以构建相关的物理解释，通常需要检测此类相位并准确估计其特征（边界，特征差异等）。然而，物理相关的情况通常伴随着低到非常低的信噪比，从而排除了标准线性滤波用于分析和去噪的标准使用，因此需要设计先进的非线性信号/图像滤波技术。此外，在处理实验物理信号/图像时，第二个限制是需要分析大量数据才能得出准确而相关的结论，需要设计快速算法。本工作基于近端算法和Stein无偏估计器原理，提出了一种具有快速算法和数据驱动的自动超参数调整的统一信号/图像非线性滤波程序。这些工具的兴趣和潜力在低约束固体摩擦信号和多孔介质多相流的工作中得到了说明。