Fan beam image reconstruction using generalized natural pixel bases [SPECT]

The purpose of this study is to represent the natural pixel basis for fan beam geometry. The image equation for generalized natural pixel basis can be described as Mq=p, where p is the projection measurement, q is the unknown estimation, and matrix M is the backprojection-projection operation. Without considering photon scatter, geometric response, and attenuation, the natural pixel representation of the projection operator for fan beam geometry is a unit strip of which central line is along the line from the center of the detector bin to the focal point. Since the backprojection operator can be different from the adjoint projection operator, one fan beam, two parallel beam backprojection operators were used to define the behavior of the backprojection functional. The singular value decomposition (SVD) reconstruction method is used to solve q in this inverse problem, and the final image is obtained by backprojecting this q into a discrete array of points. We observed that different backprojection geometries can reconstruct almost an identical image. Moreover, the use of the natural pixel basis for fan beam geometry has higher resolution than the filtered backprojection algorithm.