How to show category name that have today post?

<?php
// display the categories used on today's posts
$this_year = date('Y');
$this_month = date('m');
$this_day = date('d');
$args=array(
  'year' => $this_year,
  'monthnum' => $this_month,
  'day' => $this_day,
  'post_type' => 'post',
  'post_status' => 'publish',
  'posts_per_page' => -1,
  'caller_get_posts'=> 1
  );
$my_query = null;
$my_query = new WP_Query($args);
if( $my_query->have_posts() ) {
  while ($my_query->have_posts()) : $my_query->the_post();
    $cat_args=array('orderby' => 'none');
    $cats = wp_get_post_terms( $post->ID , 'category', $cat_args);
    foreach($cats as $cat) {
      $cat_array[$cat->term_id] = $cat->term_id;
    }
  endwhile;
}
if ($cat_array) {
  echo '<p>List of categories used on posts for '.$this_year.$this_month.$this_day.'</p>';
  foreach($cat_array as $cat) {
    $category = get_term_by('ID',$cat, 'category');
    echo '<p><a href="' . esc_attr(get_term_link($category, 'category')) . '" title="' . sprintf( __( "View all posts in %s" ), $category->name ) . '" ' . '>' . $category->name.'</a><p> ';
  }
}
wp_reset_query();  // Restore global post data stomped by the_post().
?>