Perl's file-test operators only care about the file's location on your server. If the file's URI is /username/picture.jpg, that's almost certainly not the file's full pathname on your system. That might be something like /var/www/images/username/picture.jpg, or something entirely different. You'll have to prepend $picture with the filesystem location of your picture subdirectory. Also, use a different quoting method to get rid of those backslashed quotes:

$picture = "/$username/$picture";
my $picture_path = "/var/www/images$picture"; # or whatever
if( -f $picture_path ){
  $thumb30 = qq| <img src="$picture" /> |;
} else {
  $thumb30 = qq| <img src="/images/noavatar50.png" /> |;
}
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