Iterative Tomographic Image Reconstruction Using Nonuniform Fast Fourier Transforms

Fourier-based reprojection methods have the potential to reduce the computation time in iterative tomographic image reconstruction. Interpolation errors are a limita- tion of Fourier-based reprojection methods. We apply a min-max interpolation method for the nonuniform fast Fourier transform (NUFFT) to minimize the interpolation errors. Numerical results show that the min-max NUFFT approach provides substantially lower approximation er- rors in tomographic reprojection and backprojection than Iterative methods for tomographic image reconstruction offer numerous advantages over the conventional filtered backprojection method. The late 1990's saw commercial release of 2D iterative reconstruction methods for PET and SPECT systems. The computation burden of forward and backprojection operations remains the primary hin- drance to wider use of iterative methods for fully 3D im- age reconstruction. This paper describes a new efficient approach to forward and backprojection using a combina- tion of the Fourier-slice theorem and a min-max method for the nonuniform fast Fourier transform. This approach is particularly well suited to the geometries of PET scan- ners. For most iterative reconstruction methods, each iter- ation requires computation of one "forward projection" and one "backprojection," where the forward projection is roughly a discretized evaluation of the Radon transform, and the backprojector is the adjoint of the forward projec- tor. The projection and backprojection steps traditionally

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