When a physical signal is received and used, it is most of the time noisy and not smooth. In order to manipulate it digitally, it is necessary to convert it into a smooth signal, or regularize it. A classical ways to do so is to convolve the signal with a Gaussian of fixed variance, which determines the scale at which the signal can be considered smooth. In many situations, signals are not uniformly noisy, and some parts show important local defects, while the global signal is acceptable. Similarly, industrial constraints may require only local control of the smoothing in some regions, without having a globally smooth signal. All these applications call for non-uniform smoothing. This reports proposes some methodologies to do so.