/* this is the input field */
                ...
                <input type="file" name="MoobLogoUpload" id="MoobLogoUpload" size="40" />

                <?php if ($file = $options['MoobLogoUpload']) {
                        echo "<img src='{$file['url']}' />";
                      }
                ?>
                ...




/* and this is your ajax function with the upload extra in it */

add_action('wp_ajax_test_theme_data_save', 'test_theme_save_ajax');

function test_theme_save_ajax() {

    check_ajax_referer('test-theme-data', 'security');

    $data = $_POST;
    unset($data['security'], $data['action']);

/* ### upload extra */
    if ($data['MoobLogoUpload']) {
            $overrides = array('test_form' => false);
            $file = wp_handle_upload($data['MoobLogoUpload'], $overrides);
            $data['MoobLogoUpload'] = $file;
        }

/* ### upload extra END */

    if(!is_array(get_option('test_theme'))) {
        $options = array();
    } else {
        $options = get_option('test_theme');
    }

    if(!empty($data)) {
        $diff = array_diff($options, $data);
        $diff2 = array_diff($data, $options);
        $diff = array_merge($diff, $diff2);
    } else {
        $diff = array();
    }

    if(!empty($diff)) {
        if(update_option('test_theme', $data)) {
            die('1');
        } else {
            die('0');
        }
    } else {
        die('1');
    }
}