A Hankel Transform Approach to Tomographic Image Reconstruction

We develop a relatively unexplored algorithm for reconstructing a two-dimensional image from a finite set of its sampled projections. The algorithm, which we refer to as the Hankel-transform reconstruction (HTR) algorithm, is polar-coordinate based. The algorithm expands the polar-form Fourier transform F(r, θ) of an image into a Fourier series in θ; calculates the appropriately ordered Hankel transform of the coefficients of this series, giving the coefficients for the Fourier series of the polar-form image f(p, Φ); resolves this series, giving a polar-form reconstruction; and finally, if desired, interpolates this reconstruction to a rectilinear grid. We outline the HTR algorithm and show that its performance can compare favorably to the popular convolution-backprojection algorithm.