function get_image_alt_text($image_url) {

  if ( ! $image_url )
    return '';

  if ( '/' === $image_url[0] )
    $post_id = attachment_url_to_postid(home_url() . $image_url);
  else
    $post_id = attachment_url_to_postid($image_url);

  $alt_text = get_post_meta($post_id, '_wp_attachment_image_alt', true);
  if ( '' === $alt_text )
    $alt_text = get_the_title($post_id);

  return $alt_text;

}