process can be iterated by applying the median filter to the median-filtered image, and so on. This is called *iterative median filtering.*

**Properties.**

The median is known as a robust position measure [@Tukey-Book71] in statistics, and bequeathes its robustness to the median filter for images. In particular, the median filter is known for its denoising capabilities even in the presence of some sorts of non-Gaussian (heavy-tailed) noise like salt-and-pepper or uniform impulse noise. At the same time, it can preserve sharp edges, since for pixels near an edge, the sliding window contains some pixels from either side of the edge, and the median will be on the side of the majority, thus yielding an intensity clearly belonging to one side, and not creating intermediate values.

When iterating median filtering, several phenomena are observed. On one hand, small image structures are eliminated. Whereas filtered images still show sharp edges, corners are progressively rounded.

On the other hand, non-trivial stationary patterns can appear during the iterated filtering process, most prominent with small sliding windows such as $3\times3$ or $5\times5$, but not limited to these. These so-called *root signals* have been studied, e.g., by Eckhardt [@Eckhardt-JMIV03]. The existence of such patterns is inherent 