Exponential radon transform inversion based on harmonic analysis of the Euclidean motion group

This paper presents a new method for the exponential Radon transform inversion based on harmonic analysis of the Euclidean motion group (M(2)). The exponential Radon transform is modified to be formulated as a convolution over M(2). The convolution representation leads to a block diagonalization of the modified exponential Radon transform in the Euclidean motion group Fourier domain, which provides a deconvolution type inversion for the exponential Radon transform. Numerical examples are presented to show the viability of the proposed method.