Remove Logo through custom admin page

I’ve built a custom ‘Theme Otions’ admin page by following a Sitepoint tutorial.

add_action('admin_init', 'register_and_build_fields');
function register_and_build_fields() {

add_settings_field('logo','Logo', 'logo_setting', mythemeoptions, 'main_section');

function logo_setting () {
	echo '<input type="file" name="logo" />' ;
}

In the template files I have placed:
<img src="<?php echo $options['logo']; ?>" alt="Logo" />

This works great, except I have no idea how to add a ‘Remove Logo’ option!

Any ideas? Thanks