  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.
