You're welcome Peter. It's a fun project and the products are useful at least to me in figuring out what's going on with the ice.
I agree that the median filter is the most mathematically elegant and gives the smoothest result. Also, unlike the other filters, it would work equally well during refreeze (although ice concentration probably isn't very useful during refreeze, since I guess it will quickly become 100% in most areas). However, it suffers from the disadvantage that it is slow to respond to daily changes.
As to justification, seaice.de offered a technical justification here:
http://forum.arctic-sea-ice.net/index.php/topic,1834.msg123495.html#msg123495Personally, I think the results are justification enough -- at least for use as an amateur tool. Compare the filtered images to the originals and to other evidence of the ice concentration such as satellite images. I find that the filters succeed in removing the obvious, fast-moving noise (apparently caused by cloud) and allow me to better see where the ice is thickening, thinning, or approaching the 15% threshold.
To demonstrate this again, attached is a gif of recent days, unfiltered. Look for example at the ice near the Chukchi/ESS around July 28 and again around Aug 4. Large areas become purple for a day or so and then revert back to lower concentrations. If you check WorldView, you will see that these 'purple flashes' correspond to areas and dates of thick cloud cover.
Then look at the filtered versions -- attached to following posts. They eliminate most of the purple flashes, and instead show a record of an earlier value (exactly what value they show depends on the algorithm).
This approach obviously would do a bad job at reflecting reality if low concentration anomalies were anywhere near as pervasive as high concentration anomalies. But they don't seem to be. I have been searching for them and although I do find one occasionally (see previous posts), they are rare. Indeed, this can be easily verified by looking at the high concentration area near the CAA. If low concentration artifacts were common, the filtered images would not succeed in retaining this large purple area. But, apart from a few small blemishes, they do succeed.
For additional justification about the "direction of the noise", I tried applying some inverse filters. That is, instead of for example filtering out concentrations above 90%, I filtered below 90%. The results of this exercise do not come anywhere near to reality and show just how common high concentration artifacts really are. (See following posts.)
Here is the unfiltered version: