Signal restoration by statistical soft morphology

A new set of non linear signal and image processing operators is presented. Their definition is based on the introduction of the statistical properties of Bayesian reconstruction in soft morphological operators. Statistical soft operators represent a trade-off between the noise cleaning properties of statistical morphology and the shape preservation properties of soft morphology. The main characteristic of these operators is the individualization of two parts within each structuring element (SE) according to soft morphology (i.e. `hard' and `soft' SEs), and to define on this basis a probabilistic estimation model which is a generalization of the Statistical Morphology model. Results are presented to show that the statistical soft morphological operators can be considered robust to structured noise, i.e. noise showing both statistical (e.g. additive Gaussian noise) and morphological (e.g. noise with a particular shape) structure.