The sample is the level-2 DEM of Bountiful Utah. Missing data values were replaced by the mean of the others. The standard deviation of the elevations is 1096 meters.
The compression method is Said and Pearlman's wavelet program, progcode. Lossless compression takes 5.234 bits per point (bpp) on this file.
The first display technique is a simple gray scale
Original
Lossy Compression to 1 Bit/Point, RMSE=6.0 meters
Lossy Compression to 0.1 Bit/Point, RMSE=51.7 m
Lossy Compression to 0.03 Bit/Point, RMSE=148 m
Lossy Compression to 0.01 Bit/Point, RMSE=535
Now, here are the same surfaces, plotted in 3D by Matlab.
Original
Lossy Compression to 1 Bit/Point, RMSE=6.0 meters
Lossy Compression to 0.1 Bit/Point, RMSE=51.7 m
Lossy Compression to 0.03 Bit/Point, RMSE=148 m
Lossy Compression to 0.01 Bit/Point, RMSE=535
Now, here are the differences between each level of approximation and the one below it. Note that the scales are different on each plot; otherwise the first plots would appear flat.