Radon transform inversion based on harmonic analysis of the Euclidean motion group

We present a new derivation of the spherical harmonic decomposition of the projection slice theorem using harmonic analysis of the Euclidean motion group, M(N). The Radon transform is formulated as a convolution integral over M(N). Deconvolution using harmonic analysis of M(N) leads to spherical harmonic decomposition of the projection slice theorem. The proposed method of decomposition leads to new algorithms for the inversion of the Radon transform.