Performing image reconstruction from cone-beam projections is required for both X-ray computed tomography (CT) and single photor 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 1st stage using spherical harmonics, has been proposed for the short-object problem with a huge-detector [1-2]. We have modified the method using spherical harmonics to solve the short-object problem with a midsize-detector. The 1st 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 1st derivative of the 3D Radon transform from masked data using spherical harmonics (similar to [1-2]), and 1c) obtaining complete data of the 1st 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.
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