How to change the preview in the video?

Question

YouTube

Good afternoon! According to this article, I am optimizing the loading of a website page from a YouTube video.
Here is the jQuery code

$(function() {
    $(".youtube").each(function() {
        // Based on the YouTube ID, we can easily find the thumbnail image
        $(this).css('background-image', 'url(http://i.ytimg.com/vi/' + this.id + '/sddefault.jpg)');

        // Overlay the Play icon to make it look like a video player
        $(this).append($('<div/>', {'class': 'play'}));

        $(document).delegate('#'+this.id, 'click', function() {
            // Create an iFrame with autoplay set to true
            var iframe_url = "https://www.youtube.com/embed/" + this.id + "?autoplay=1&autohide=1";
            if ($(this).data('params')) iframe_url+='&'+$(this).data('params');

            // The height and width of the iFrame should be the same as parent
            var iframe = $('<iframe/>', {'frameborder': '0', 'src': iframe_url, 'width': $(this).width(), 'height': $(this).height() })

            // Replace the YouTube thumbnail with YouTube HTML5 Player
            $(this).replaceWith(iframe);
        });
    });
});

That is, this code loads the preview first, and when you click on the picture, it already loads the video.
The problem is that not all videos have a picture, some have it instead of a picture.
Can you please tell me if it is possible for such videos to set up their own picture?