On the Exponential Radon Transform and Its Extension to Certain Functions Spaces

We investigate the exponential Radon transform on a certain function space of generalized functions. We establish certain space of generalized functions for the cited transform. The transform that is obtained is well defined. More properties of consistency, convolution, analyticity, continuity, and sufficient theorems have been established.

AN ANALYTICAL INVERSION OF THE 180° EXPONENTIAL RADON TRANSFORM WITH A NUMERICALLY GENERATED KERNEL

This work presents an inversion algorithm for the exponential Radon transform (ERT) over 180° range of view angles. The algorithm can be applied to two-dimensional parallel beam geometry in single photon emission computed tomography. First the differentiation of the ERT over π is backprojected. A convolutional relation between this backprojected differentiation and the original image is then established. In order to invert the convolution relation, the least-squares method is utilized to obtain a numerically generated filtering kernel, which readily restores the original image. The advantages of the proposed algorithm are, first, it only requires half the view angles of the conventional inversion algorithm, second, it deals with truncation in ERT data in certain situations, and third, the numerically generated filtering kernel can be pre-calculated and stored for later applications. The algorithm is an analytical approach except for the pre-calculated inverse kernel.