An efficient Fourier method for 3-D radon inversion in exact cone-beam CT reconstruction.
The radial derivative of the three-dimensional (3-D) radon transform of an object is an important intermediate result in many analytically exact cone-beam reconstruction algorithms. We briefly review Grangeat's approach for calculating radon derivative data from cone-beam projections and then present a new, efficient method for 3-D radon inversion, i.e., reconstruction of the image from the radial derivative of the 3-D radon transform, called direct Fourier inversion (DFI). The method is based directly on the 3-D Fourier slice theorem. From the 3-D radon derivative data, which is assumed to be sampled on a spherical grid, the 3-D Fourier transform of the object is calculated by performing fast Fourier transforms (FFT's) along radial lines in the radon space. Then, an interpolation is performed from the spherical to a Cartesian grid using a 3-D gridding step in the frequency domain. Finally, this 3-D Fourier transform is transformed back to the spatial domain via 3-D inverse FFT. The algorithm is computationally efficient with complexity in the order of N3 logN. We have done reconstructions of simulated 3-D radon derivative data assuming sampling conditions and image quality requirements similar to those in medical computed tomography (CT).
Siemens AG, Erlangen, Germany. schaller@nt.e-technik.uni-erlangen.de
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D000465:Algorithms; D016477:Artifacts; D003198:Computer Simulation; D005583:Fourier Analysis; D006257:Head / Q000000981:diagnostic imaging; D006801:Humans; D007089:Image Enhancement / Q000379:methods; D007091:Image Processing, Computer-Assisted / Q000706:statistics & numerical data*; D015233:Models, Statistical; D019047:Phantoms, Imaging; D014057:Tomography, X-Ray Computed / Q000706:statistics & numerical data*