Cone-beam image reconstruction using spherical harmonics: Short-object problem with midsize-detector

Performing image reconstruction from cone-beam projections is required for both X-ray computed tomography (CT) and single photon emission computed tomography (SPECT). The Grangeat´s algorithm consists of three stages: (1) obtaining the first derivative of the plane integral (3D Radon transform) from cone-beam projections, (2) rebinning the data and calculating the second derivative, and (3) reconstructing the image using the 3D Radon backprojection. Recently, a new implementation method of Grangeat´s algorithm for the 1^st stage using spherical harmonics, has been proposed for the short-object problem with a huge-detector. We have modified the method using spherical harmonics to solve the short-object problem with a midsize-detector. The 1^st stage can be described by the following three steps: (1a) masking the cone-beam projections at each cone vertex position, (1b) calculating partial data of the 1^st derivative of the 3D Radon transform from masked data using spherical harmonics, and (1c) obtaining complete data of the 1^st derivative of the 3D Radon transform using the partial data at plural cone vertex positions. If the trajectory of the cone vertex satisfies Tuy´s data sufficiency condition, the proposed algorithm provides an exact reconstruction. Computer simulations were performed to verify the approach