How to inject @EJB, @PersistenceContext, @Inject, @Autowired, etc in @FacesConverter?

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?