Analytical algorithm for 3D cone-beam SPECT reconstruction with uniform attenuation correction

The authors present a new approach to three-dimensional (3D) image reconstruction, extending their results for the exponential Radon transform to inversion of the exponential cone-beam transform, which can serve as a mathematical model for 3D SPECT imaging. The authors apply a circular cone-beam scan and assume constant attenuation inside a convex area with a known boundary, which is satisfactory in brain imaging. Their method requires two computation steps: backprojection and filtering. The filter is implemented in the frequency domain and requires 2D Fourier transform of transverse slices. In order to obtain a shift invariant cone-beam projection-backprojection operator, the authors resort to an approximation, assuming that the collimator has a relatively large focal length. Nevertheless, numerical experiments demonstrate surprisingly good results for detectors with relatively short focal lengths. The use of a wavelet-based filtering algorithm greatly improves the stability to Poisson noise