Fast computation of Fourier-Bessel transforms

The Fourier-Bessel transforms (also designated as Hankel transforms) arise in numerous signal processing problems. They are particularly important in image analysis, reconstruction of unknown media from projections, synthesis of waves from their spatial spectrum. Three basic techniques (and a number of possible variations) for calculating Fourier-Bessel transforms have been recently developed by us. The present paper provides a brief review of these methods and a discussion of their accuracy. Test calculations illustrate this analysis and yield further indications for proper application of the proposed methods.