SPLINE-BASED INVERSE RADON-TRANSFORM IN 2-DIMENSIONS AND 3-DIMENSIONS

While the exact inverse Radon transform is a continuous integral equat ion, the discrete nature of the data output by tomographic imaging sys tems generally demands that images be reconstructed using a discrete a pproximation to the transform. However, by fitting an analytic functio n to the projection data prior to reconstruction, one can avoid such a pproximations and preserve and exploit the continuous nature of the in verse transform. We present methods for the evaluation of the inverse Radon transform in two and three dimensions in which cubic spline func tions are fit to the projection data, allowing the integrals that repr esent the filtration of the sinogram to be carried out in closed form and also eliminating the need for interpolation upon backprojection. M oreover, in the presence of noise, the algorithm can be used to recons truct directly from the coefficients of smoothing splines, which are t he minimizers of a popular curve-fitting measure. We find that the 2D and 3D direct-spline algorithms have superior resolution to their 2D a nd 3D FBP counterparts, albeit with higher noise levels, and that they have slightly lower ideal-observer signal-to-noise ratios for the det ection of a l-cm, spherical lesion with a 6:1 lesion-background concen tration ratio.