Parent Image

Hi there,
The code below returns a list of [posts] Parent category titles which works.
What I can’t figure out is how to add the thumbnail (but I’ll take any size) image for each one.
It’s probaly simple but I can’t figure it out.
Many thanks

<?php
/* template name: ParentCatTemplate */
get_header(); ?>
    <?php
// get_categories() function will return all the categories
     $upaae_categories = get_categories( array(  'orderby' => 'name',  'order' => 'ASC' ) ); 
          foreach( $upaae_categories as $single_cat ) {  if($single_cat->parent < 1) 
          // Display if parent category and exclude child categories  
              {$category_link = sprintf( '<a href="%1$s" alt="%2$s">%3$s</a>', esc_url( get_category_link( $single_cat->term_id ) ),  
              esc_attr( sprintf( 'View all posts in %s', 'textdomain' ), $single_cat->name ),  esc_html( $single_cat->name ));  
            echo 
             sprintf( $category_link ).'</br>';  } } 
    ?>
<?php get_footer(); ?>