How can I inject a dependency like @EJB, @PersistenceContext, @Inject, @AutoWired, etc in a @FacesConverter? In my specific case I need to inject an EJB via @EJB:
@FacesConverter
public class MyConverter implements Converter {
  @EJB
  protected MyService myService;    
  @Override
  public Object getAsObject(FacesContext context, UIComponent component, String value) {
    // myService.doSomething
  }
}
However, it didn't get injected and it remains null, resulting in NPEs. It seems that @PersistenceContext and @Inject also doesn't work.
How do I inject a service dependency in my converter so that I can access the DB?