Scale and smooth low res textures

I have one very low res texture in my mesh, with some big ugly pixels all over. So I opened that image on Gimp and scaled it with cubic interpolation (smoothes the scaling). Now my texture looks smooth with no ugly big pixels. This is exactly the effect that I wanted.

But now I have this very big texture file to move around.

Is there anyway I can do the same thing I did in Gimp using Blender? I checked the manual on both the properties that I can set on a texture as well on texture Nodes. But I didn’t find anything that could do this. Is there something I’m missing?