Don't believe it's shepherd's purse as that name, at least locally applies to a triangular seed pod, hence the shepherd's purse. Looks like Berteroa incana on first glance, again widely established US but originally from Europe; but not familiar with Italian Brassicaceae(Cruciferae). If B. incana, then 4 white petals are deeply divided (two lobed) or knotched, which isn't really apparent in your photo. Harry
