Add about 1/4 of the salmon to a food processor with the yogurt and lemon juice. Pulse until the mixture forms into a thick paste. This will hold the salmon patties together. Add the remaining salmon and pulse just a couple of times so the salmon is in smaller pieces, about 1/4 inch thick, but not fully processed. You want the salmon to have some texture and larger pieces.
Remove from the food processor and gently stir in the onions, parsley, paprika, salt, garlic powder, onion powder, and black pepper. Once combined, divide the mixture into four patties about 1 inch thick, pressing them together with your hands. Optional: For a crunchy burger, press each burger into Panko breadcrumbs to create a crunchy exterior. You will need 1/3-1/2 cup total for 4 burgers.