Select A Radio Button By Clicking An Image

I have a form that shows some images with a radio button associated with each one. I would like to give them the option to click on the image to select the radio, but not sure the easiest way to pull it off.

I was assuming I add a OnClick to each image and use getelementbyid to check the button, but since all the radiobuttons have the same id (so they can only choose one) I am not sure how to make the correct radiobutton become checked.

Hope this makes sense, here is the simplified sample form:

<form>
<img src="image1.gif" />
<input id="radiobutton" type="radio" value="Image1" />
<img src="image2.gif" />
<input id="radiobutton" type="radio" value="Image2" />
<img src="image3.gif" />
<input id="radiobutton" type="radio" value="Image3" />
<img src="image4.gif" />
<input id="radiobutton" type="radio" value="Image4" />
</form>