Frequency weighted least squares reconstruction of truncated transmission SPECT data

A least squares technique for reconstructing truncated data is presented. The method involves including the ramp filter into the system matrix. The sinogram is extrapolated with zeros for filtering but extrapolated values are not considered during backward and forward projections. The new matrix leads to a frequency weighted least squares criterion. Tikhonov regularization and a priori information are considered. For the O-order regularization, the resulting images are biased but it is shown that this bias is recovered by a simple scaling process. First and second order regularizations provide true restoration. The technique is applied to simulated and real transmission SPECT data. Results show that the frequency least squares criterion is a valuable approach for efficiently reconstructing truncated sinograms