A Fourier reconstruction algorithm with constant attenuation compensation using 180 degrees acquisition data for SPECT

In this paper, we develop an approximate analytical reconstruction algorithm that compensates for uniform attenuation in 2D parallel-beam SPECT with a 180-degree acquisition. This new algorithm is in the form of a direct Fourier reconstruction. The complex variable central slice theorem is used to derive this algorithm. The image is reconstructed with the following steps: first, the attenuated projection data acquired over 180 degrees are extended to 360 degrees and the value for 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 an analytic function interpolated from an extension of the 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 360-degree full-scan algorithm are provided.