An iterative algorithm using a natural pixel representation of the attenuated radon transform

Simultaneous transmission-emission imaging using a three detector SPECT system typically must reconstruct attenuation maps of the thorax using truncated transmission projections. It has been observed in simulations that the use of natural pixels significantly improves the accuracy and the image quality of reconstructed truncated projections. The purpose of this work is to investigate the use of natural pixels to reconstruct attenuation corrected emission data using attenuation factors calculated from a natural pixel representation of the reconstructed truncated transmission data. The reconstruction algorithm for both transmission and emission reconstructions is based on the assumption that a continuous image can be obtained by backprojecting the discrete array q, which is the least squares solution to Mq=p where p is the array of discrete measurements. The matrix M represents the operator obtained from the backprojection operator followed by the projection operator using the natural pixel basis. The conjugate gradient algorithm is used to solve the equation Mq=p, and the final image is obtained by sampling the continuous backprojection of the solution q at a discrete array of points