"I have tried...."

is as uninformative as a classic error-in-posting, namely:

"...doesn't work."

Try showing us what you've tried (minimal cases which fail, please).

#!/usr/bin/perl --

use strict;
use warnings;
use HTML::TreeBuilder;

my $html = <<'__HTML__';
<a href="http://www.yahoo.com" target=_blank><img
src="http://us.i1.yimg.com/nw.gif" 
alt="Open this result in new window">ANCHOR TEXT</a>

<a href="http://www.yahoo.com" target=_blank><img
src="http://us.i1.yimg.com/nw.gif" 
alt="Two clues for the price of one"></a>
__HTML__


{
  my $h = HTML::TreeBuilder->new_from_content($html);

  for my $link ( $h->look_down( _tag => q{a}, href => 'http://www.yaho
+o.com' ) )
  {
    print $link->attr('href'),"\n";
    my $text = $link->as_trimmed_text;
    unless ($text) {
      $text = join ' ',
        map { $_->attr('alt') } $link->look_down( alt => qr/^.+$/ );
    }
    print "$text\n\n";
  } ## end for my $link ( $h->look_down...)

}

__END__
[download]

The output is :

http://www.yahoo.com; ANCHOR TEXT

http://www.yahoo.com; Two clues for the price of one

But the desired output is :

http://www.yahoo.com; ANCHOR TEXT

http://www.yahoo.com; IMAGE (indicating no anchor text and also presence of img tag within anchor tag )

Any ideas?

You have just copied the code from Re^2: anchor text match literatim (except for some mild massaging of the input). What have you tried?