Reconstruction for fan beam with an angular-dependent displaced center-of-rotation

A convolutional backprojection algorithm is derived for a fan beam geometry that has an angular-dependent displacement in its center-of-rotation from the midline of the fan beam. In both x-ray computed tomography and single photon emission computed tomography, misalignment can occur when the mechanical center-of-rotation is not colinear with midline of the fan beam. In some cases the shift in the center-of-rotation is constant for every angle, whereas, in other cases it varies with angular position. Standard reconstruction algorithms, which directly filter and backproject the fan beam data without rebinning into parallel beam geometry, have been derived for a geometry having its center-of-rotation at the midline of the fan beam. However, in the case of any misalignment of the center-of-rotation, if these conventional reconstruction algorithms are used to reconstruct the fan beam projections, structured artifacts and a loss of resolution will result. Simulations are performed that illustrate these artifacts and demonstrate how the new algorithm corrects for this misalignment. A method for estimating the parameters of the fan beam geometry, including the angular-dependent shift in the center-of-rotation, is also described.