preg_replace to link all images in content?

Hello, I’m trying make a short plugin to replace all <img> tags in the_content with <href><img> tags. Is this possible with preg_replace?

More specifically, i’d like to place every:
<img src="anyfile">
With
<a href="anyfile"><img src="anyfile"></a>

I’m not experienced with regex, but here is what i have so far, which isn’t working:

<?php
define("IMAGE_FILETYPE", "(bmp|gif|jpeg|jpg|png)", true);

function everyimage_create($string){
	$pattern = '/<a(.*?)img(.*?)src="(.*?).(bmp|gif|jpeg|jpg|png)"(.*?)>/i';
  	$replacement = '<a$1$2href="$3.$4" rel=\'lightbox[imagegroup]\'$5><a img src=$3.$4"></a>';
	return preg_replace($pattern, $replacement, $string);
}

add_filter('the_content', 'everyimage_create');

?>

The overall goal is to have embedded images be clickable, so that they open in their original size using lightbox (or slimbox, etc.)

Thanks for any help or tips.