The discrete periodic radon transform

In this correspondence a discrete periodic Radon transform and its inversion are developed. The new discrete periodic Radon transform possesses many properties similar to the continuous Radon transform such as the Fourier slice theorem and the convolution property etc. With the convolution property a 2-D circular convolution can be decomposed into 1-D circular convolutions hence improving the computational efficiency. Based on the proposed discrete periodic Kadon transform we further develop the inversion formula using the discrete Fourier slice theorem. It is interesting to note that the inverse transform is multiplication free. This important characteristic not only enables fast inversion hut also eliminates the finite-word-length error that may be generated in performing the multiplications.