Grind the shrimp in a food processor. Add the onions, garlic powder, cayenne pepper, and salt. Mix well. Heat the olive oil in a large fry pan over medium heat.
While oil heats, form the shrimp mixture into patties. Add to the pan. Fry on each side until patties turn pink and opaque.
Serve on toasted hamburger buns with tarter sauce, lettuce, tomato, and pickle.