Latest Posts per Category as Unordered List in Wordpress

<div class="latest-posts">
<?php
$cat_args=array(
  'include' => '1,2,3,4', // categories to display separated by commas
  'orderby' => 'ID', // ordered by category id - options - ID, name, slug, count, term_group
  'order' => 'ASC' // order ascending
   );
$categories=get_categories($cat_args);
  foreach($categories as $category) {
    $args=array(
      'showposts' => 4, // number of posts to display
      'category__in' => array($category->term_id),
      'ignore_sticky_posts'=>1 // number of sticky posts to ignore in the listing
    );
    $posts=get_posts($args);
      if ($posts) {
        echo '<ul class="preview"><div class="preview-header"><div class="category"><a href="' . get_category_link( $category->term_id ) . '" title="' . sprintf( __( "View all posts in %s" ), $category->name ) . '" ' . '>' . $category->name.'</a></div></div>';
        foreach($posts as $post) {
          setup_postdata($post); ?>
        <li>
        <div class="image"><a href="<?php the_permalink(); ?>"><?php the_post_thumbnail( 'small' ); ?></a></div>
        <h4 class="title"><a href="<?php the_permalink() ?>" rel="bookmark" title="<?php the_title_attribute(); ?>"><?php the_title(); ?></a></h4>
        </li>

          <?php
                }
echo '</ul>';       }
            }
?>
</div>