Smoothing DEM using GRASS?

How about John Stevenson's r.denoise, from the GRASS AddOns wiki:

r.denoise denoises (smooths/despeckles) topographic data, particular DEMs derived from radar data (including SRTM), using Xianfang Sun's denoising algorithm. It is designed to preserve sharp edges and to denoise with minimal changes to the original data.

I read further from this website (that I also give credit for the above animation) that a more generic method would be to use an Esri ASCII Grid file. The location of mdenoise (downloaded from Sun's website) needs to be in your PATH variable (e.g., Windows users: drop MDenoise.exe in the bin folder with your OSGeo4w or FWTools install). Then, for example, you can use the following shell command to process the ASCII grid file:

# gdal_translate -of AAIGrid my_dem.tif my_dem.asc      # convert to .asc
mdenoise -i my_dem.asc -n 5 -t 0.99 -o my_dem_DN.asc    # denoise
# gdal_translate -of GTiff my_dem_DN.asc my_dem_DN.tif  # convert back to .tif

Denoise is under GNU license, see here

Tom Patterson, the lead cartographer at the U.S. National Parks Service has some excellent tutorials on working with DEM data to make beautiful shaded reliefs. Part of his workflow involves using Natural Scene Designer and Adobe Photoshop.

For my own workflow I like to use GDAL to resample the size of the DEM before rendering a shaded relief. This often helps with reducing the amount of detail and noise, not to mention file size. I have a tutorial on Github that demonstrates how to do this.

Basically the process is to specify a new width and/or height (in pixels) for an output DEM that is smaller than the original file size. For example doing:

gdalwarp -ts 3000 0 -r bilinear kings_canyon_2228.tif kings_canyon_2228_rs.tif

Will reduce the width of the DEM to 3000 pixels from the original width of 3800 pixels. Setting the height to 0 will let GDAL determine the best height of the new file based on the original's aspect ratio.

I used GIMP plugin wavelet noise reduction tool and I get good results and fast:

GIMP Plugin Wavelet noise reduction