It's interesting because it looks like pic_id is broken json. We can still get the data with a regex:
$str = <<<EOF
<div class="pic" style="top:0px;left:0px;height:149px;" data='{"pic_id":"06e50224ab189";}' pic-descr=" this title " data-index="0">
</div>
EOF;
$html = str_get_html($str);
$div = $html->find('.pic', 0);
if(preg_match('/:"(.*?)"/', $div->data, $m)){
echo "pic_id is: " . $m[1] . "
";
}
echo "pic-descr is: " . $div->{'pic-descr'} . "
";
If the json were not broken you could do:
json_decode($div->data)->pic_id