<a href="#"><img src="image.png"  /></a>  ==> this should not have a bottom-border on hover
<a href="#">regular text link</a> ==> this should have a bottom-border on hover

#sidebar a:hover {
  border-bottom: 1px dotted red;
}
#sidebar a:hover img {
  border-bottom: none;
}

#sidebar a:hover { text-decoration: underline; }
#sidebar a:hover img { text-decoration: none; }

a img {position:relative; top: Npx}, where N is the hover border thickness

$('#sidebar a:has(img)').addClass('image-link');

#sidebar a:hover {
  border-bottom: 1px dotted red;
}
#sidebar a.image-link:hover {
  border-bottom: none;
}

$text = preg_replace('#<a(.*?)<img(.*?)/>(.*?)</a>#is', "<a class='imgshow' \1 <img\2 />\3</a>", $text);