Wordpress - How to get the custom header image's alt text?

/**
 * Get custom header's alt data.
 * 
 * @link    http://wordpress.stackexchange.com/q/151850/1685
 * 
 * @return  string
 */
function wpse_151850_get_header_image_alt() {
    $attachment_id = 0;

    if ( is_random_header_image() && $header_url = get_header_image() ) {
        // For a random header, we have to search for a match against all headers.
        foreach ( get_uploaded_header_images() as $header ) {
            if ( $header['url'] == $header_url ) {
                $attachment_id = $header['attachment_id'];
                break;
            }
        }

    } elseif ( $data = get_custom_header() ) {
        // For static headers, less intensive approach.
        $attachment_id = $data->attachment_id;
    } 

    if ( $attachment_id ) {
        $alt = trim( strip_tags( get_post_meta( $attachment_id, '_wp_attachment_image_alt', true ) ) );

        if ( ! $alt ) // Fallback to caption (excerpt)
            $alt = trim( strip_tags( get_post_field( 'post_excerpt', $attachment_id ) ) );
        if ( ! $alt ) // Fallback to title
            $alt = trim( strip_tags( get_post_field( 'post_title', $attachment_id ) ) );
    } else {
        $alt = '';
    }

    return $alt;
}