A scalable architecture for implementing the fast discrete periodic radon transform for prime sized images

The Discrete Periodic Radon Transform (DPRT) has many important applications in image processing that are associated with reconstructing objects from projections (e.g., computed tomography [1]) or image restoration (e.g., [2]). Thus, there is strong interest in the development of fast algorithms and architectures for computing the DPRT. This paper introduces a scalable hardware architecture and associated algorithm for computing the DPRT for prime-sized images. For square images of size N × N, N prime, the DPRT requires N² (N - 1) additions for calculating image projections along a minimal number of prime directions. The proposed approach can compute the DPRT in [N/2^h] N + 2N + h clock cycles, h = 1, ..., [log₂ N], where h is a scaling factor that is used to control the required hardware resources that are needed to implement the fast DPRT. Compared to previous approaches, a fundamental contribution of the proposed architecture is that it allows effective implementations based on different constraints on the resources.