Computational complexity lower bounds of certain discrete Radon transform approximations

For the computational model where only additions are allowed, the Ω(n log n) lower bound on operations count with respect to image size n × n is obtained for two types of the discrete Radon transform implementations: the fast Hough transform and a generic strip pattern class which includes the classical Hough transform, implying the fast Hough transform algorithm asymptotic optimality. The proofs are based on a specific result from the boolean circuits complexity theory and are generalized for the case of boolean ∨ binary operation.