Displace adds an extra noise Anybody knows if I can limit the noise generate by displace modifier? On my test I have used a picture like following.

But the results are like this:

There seems to be unexpected noise on the edges. The problem comes worst when I try to subdivide the plane over 100 times. Subdividing I'm using to make smooth edges.
Here is a screen capture from original file showing that there were only two colors used on the edges. The yellow rectangle on blender picture shows the place where this part has been taken when the original image has been zoomed in 600%.
Why do you need displacement?
For a shape like this it would be a lot easier to create clean geometry and with a lot less vertices.
Or trace the shape as path in a vector drawing program (inkscape, illustrator, etc) and save as SVG to import back to blender.
Diagonal lines will always be jagged in raster formats (and in this case you see clearly how compression creates other artifacts).