The easiest way to accomplish this would be to apply an inline style to your menu. For example if you have a menu as follow:
<li class="parent"><a href="#">Item 1</a>
<ul class="level-1">
<li><a href="#">Sub Item 1</a></li>
<li><a href="#">Sub Item 2</a></li>
<li><a href="#">Sub Item 3</a></li>
</ul>
</li>
then you can do something like this:
<li class="parent"><a href="#" style="background-image:url(images.jpeg);">Item 1</a>
<ul class="level-1">
<li><a href="#">Sub Item 1</a></li>
<li><a href="#">Sub Item 2</a></li>
<li><a href="#">Sub Item 3</a></li>
</ul>
</li>