On the convolution property of a new discrete radon transform and its efficient inversion algorithm

In this paper, a new discrete Radon transform (DRT) and the inverse transform algorithm are proposed. The proposed DRT preserves most of the important properties of the continuous Radon transform, for instance, the Fourier Slice theorem, convolution property, etc. With the convolution property, the computation of a two-dimensional (2-D) cyclic convolution can be decomposed as a number of one-dimensional (1-D) ones, hence greatly reduces the computational complexity. Based on the proposed DRT, we further derive the inverse transform algorithm. It is interesting to note that it is a multiplication free algorithm that only additions are required to perform the inversion. This important characteristic not only reduces the complexity in computing the inverse transform, but also eliminates the finite word length error that may be generated in performing the multiplications.