1. Mix salmon, wheat berries, whole-wheat breadcrumbs, and 3 egg whites. Form into 8 patties; chill for 15 minutes. Dip cakes in remaining egg white and dredge in panko.
2. Preheat oven to 425°. Combine yogurt, dill, and lemon juice; set aside.
3. Bake salmon cakes in middle of oven for 15 minutes or until heated through and tops are golden. Preheat broiler; brown tops of cakes for 10–20 seconds. Serve with cucumbers, pickled ginger, and dill sauce.