Styling first paragraphs – functions.php question

I’ve separately styled the first paragraphs of my posts using the following in functions.php:

function first_paragraph($content){
	return preg_replace('/<p([^>]+)?>/', '<p$1 class="lead">', $content, 1);
}
add_filter('the_content', 'first_paragraph');

However, very often, the posts have images as the first paragraph – which means that the image paragraph gets the new “class=lead” style (which is useless because it’s just an image), but the actual first text paragraph does not.

What can I do to modify this code so that it will check to see if the first paragraph contains an image, and then ignore that paragraph? What I would like, is to treat the first text-only paragraph as the one that should be styled with “class=lead”.

Any suggestions?