A frequency domain polar back-projection algorithm

In many applications, it is necessary to reconstruct a multidimensional object from a set of its projections. In applications such as imaging radar, x-ray photographs, and radio astronomy, the information can be defined over a radial sector. This occurs when the information is gathered in a polar (magnitude, angle) rather than a Cartesian format. In such cases, the method of back-projection can be employed to achieve maximum utilization from the collected samples. Presented here is an implementation of a two-dimensional Fourier transform using the back-projection technique. This is done with the use of a one-dimensional fast Fourier transform, a direct summation, and a simple one-dimensional interpolation. This implementation also has the advantage of requiring storage for only one slice of frequency information at a time, which means it is also adaptable to parallel processing techniques.