An SVD reconstruction algorithm using a natural pixel representation of the attenuated Radon transform

The purpose of this work was 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 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 M matrix represents the operator obtained from the backprojection operator followed by the projection operator using the natural pixel basis. A singular value decomposition was used to solve the equation Mq=p, and the final image was obtained by sampling the continuous backprojection of the solution q at a discrete array of points. Computer simulations showed that accurate attenuation corrected reconstructions could be obtained using a natural pixel representation of the attenuated Radon transform for a variable attenuator