You cannot really, unless you have the original PSD or Raster or Vector file.
If you do have one of the above formats of the file, then you can simply open it and then "save as" and choose a higher color bit (lets say instead of 16 bit color, save as 32 bit color etc).
If you dont have the original file, then the only proper way to get a higher quality image is to bring the design to a graphics person and ask them to design it.
You still can find pics with high quality on Google image. There was a method shared here , if i can remember is something like this inurl:istock keyword. Use this and you will find good quality images.