Analytical reconstruction algorithm with constant attenuation compensation using 180/spl deg/ acquisition data

In this paper, we develop an analytical reconstruction algorithm that compensates for uniform attenuation in 2D parallel-beam SPECT with 180 acquisition. This new algorithm is in the form of direct Fourier reconstruction. The complex central slice theorem and contour integral are used in deriving this algorithm. The image is reconstructed with the following steps. First, the attenuated projection data acquired over 180deg are extended to 360deg and the uniform attenuator is changed to a negative value. The Fourier transform (FT) of the image in polar coordinates is obtained from the Fourier transform of the extended projection data according to the complex central slice theorem. Finally, the image is obtained by performing a 2D inverse Fourier transform. Computer simulations and comparison studies with a 360deg full-scan algorithm are provided