How about this for a solution that doesn't involve WMI.
#This will retrieve all processes by userid
$UserName="lsqa2setup"
$Processes=get-process|selectprocessname,Id,@{l="Owner";e={$owners[$_.id.tostring()]}}|Where-Object{$_.owner-eq$UserName}
#then filter the value you needForeach($Processin$Processes) { Write-host$Process.ProcessName }