Using this instructable, you can create a hidden desktop shortcut with the judicious use of The Gimp, or some other full-featured editor.
Step 1: Choose your background
Odds are you have a favorite picture as your background. Once you've selected one, open the original file in the GIMP. We'll use this picture for the icon. Also, check your screen resolution (System-->Preferences-->Screen Resolution) and write down what you find (Mine is set to 1024x768). The screen resolution is only important if the image you use is bigger than your resolution. On my PC, the image size is 1920x1440, much larger than my screen resolution of 1024x768.
Step 2: Resize Background Picture
If your picture is bigger than your background, or if you're stretching a smaller image to fill your background, this step is for you. If your image is exactly the same size as your screen resolution or smaller, ignore this step.
With the background picture open, select image-->scale image. Scale the image to exactly the size you saw in Screen Resolution. In my case this resolution is 1024x768.
Step 3: Select small area of background picture
Once you've scaled the image to the right size, use the selector tool in the Gimp to select a square 48 pixels by 48 pixels. As you use the selector tool, you'll see the area in pixels displayed at the bottom of the window. You can choose any part of the picture. Ctrl+C to copy just this area to the clipboard.
Step 4: Create new file in the Gimp
Now we'll create a 48x48 pixel image in the Gimp. While in the Gimp, ctrl+n for a new document, type in 48x48 in the Width and Height boxes. You'll end up with a blank square. Use Ctrl+V to paste the area selected in the previous step. You'll end up with a tiny bit of your original picture. Save the resulting image as icon.png.