Is it possible to set the opacity of a background image without affecting the opacity of child elements?

Example

All links in the footer need a custom bullet (background image) and the opacity of the custom bullet should be 50%.

HTML

<div id="footer">
    <ul>
        <li><a href="#">Link 1</a></li>
        <li><a href="#">Link 2</a></li>
        <li><a href="#">Link 3</a></li>
        <li><a href="#">Link 4</a></li>
        <li><a href="#">Link 5</a></li>
    </ul>
</div>  

CSS

#footer ul li {
    background: url(/images/arrow.png) no-repeat 0 50%;
}  

What I've Tried

I tried setting the opacity of the list items to 50%, but then the opacity of the link text is also 50% - and there doesn't seem to be a way to reset the opacity of child elements:

#footer ul li {
    background: url(/images/arrow.png) no-repeat 0 50%;
    /* will also set the opacity of the link text */        
    opacity: 0.5;
}

I also tried using rgba, but that doesn't have any effect on the background image:

#footer ul li {
    /* rgba doesn't apply to the background image */
    background: rgba(255, 255, 255, 0.5) url(/images/arrow.png) no-repeat 0 50%;
}