Using your themes hook locations with a conditional tag for the home page, you can display an image or any content in any hook location based on specific conditions like on the home page only.

Display Content Home Page Only

add_action('genesis_before_sidebar_widget_area', 'wpsites_home_function');
function wpsites_home_function() {
if (is_home() )
    echo '<div class="sidebar-home"><img src="http://yourdomain.com/wp-content/uploads/2013/03/yourimage.png" alt="sidebar home logo" /></div>';
}