Computation of the forward and inverse Radon transform via the central slice theorem employing a nonscanning optical technique
Rupert C. D. Young, Christopher Reginald Chatwin · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1996
The forward Radon transform operating on edge enhanced images is identical to the Hough transform in its (rho) -(phi) parametrization. The inverse operation may be used to recover an image from its projection data, acquired using tomography. Both forward and inverse operations may be efficiently computed by exploiting the central slice theorem, the major computational operations then becoming two dimensional and one dimensional Fourier transformation with an intervening coordinate conversion. The paper describes a non-scanning optical arrangement to implement both the forward and inverse Radon transform which may thus be used to compute both the Hough transform of image data and, by exchanging the input and output sections, the reconstruction of projection data. Simulations of the computation of the Hough transform via the central slice theorem are presented which include pixel interpolation in the polar mapping coordinate conversion to more closely approximate the analogue transformation which may be accomplished by the optical processor.