Under the blind assumption that your data won't be changing too much or becomes 'faulty' (otherwise you'd be using a parser right?) then something like this ought do

my $re = qr{
  (?: <img \s+ .*? src=" ([^"]+) " .*? > )?
  <a \s+ .*? href=" ([^"]+) " .*? >
}x;

$in =
  '<td><img src="foo.jpg"><a href="index3.html">New index</a></td>';

my($href, $img) = grep defined, reverse $in =~ $re;

print "href - $href\nimg  - $img\n";

$in = '<td><a href="index3.html">New index</a></td>';

($href, $img) = grep defined, reverse $in =~ $re;

print "href - $href\nimg  - $img\n";

__output__

href - index3.html
img  - foo.jpg
href - index3.html
img  -
[download]

See. perlre for more info.
HTH

_________
broquaint