A harmonic decomposition reconstruction algorithm for spatially varying focal length collimators

Spatially varying focal length fan-beam collimators can be used in single p hoton emission computed tomography to improve detection efficiency and to r educe reconstruction artifacts resulting from the truncation of pi-ejection data. It has been proven that there exists no convolution backprojection a lgorithm for this type of collimator, so a complicated interpolation betwee n two nonparallel projection rays is necessary for existing algorithms. The interpolation may generate blurring and artifacts in the reconstructed ima ges. Based on a harmonic decomposition technique and the translation proper ty of Fourier series, a semifrequency resampling technique is proposed to a void the above mentioned interpolations. By this technique, the harmonic de composition of projection data for spatially varying focal length fan-beam collimators has the same form as that for parallel-beam collimators in the semifrequency domain (Fourier transform with respect to angular variables o nly), An alternative version of the inverse Cormack transform is then propo sed to reconstruct the images. The derived reconstruction algorithm was imp lemented in a Pentium II/266 PC computer. Numerical simulations demonstrate d its efficiency (3 s for 128 x 128 reconstruction arrays) and its robust p erformance (compared to the existing algorithms).