Choice of initial conditions in the ML reconstruction of fan-beam transmission with truncated projection data

We investigate the effects of initial conditions in the iterative maximum-likelihood (ML) reconstruction of fan-beam transmission projection data with truncation. In an iterative ML reconstruction, the estimate of the transmission reconstructed image in the previous iteration is multiplied by some factors to obtain the current estimate. Normally, a flat initial condition (FIC) or an image with equal positive pixel values is used as initial condition for an ML reconstruction. Usage of FIC has also been perceived as a way of preventing any bias on the reconstruction which may have come from the initial condition. When projection data have truncation, we show that using an FIC in an ML iterative reconstruction can introduce a bias to the reconstruction inside the densely sampled region (DSR), whose projection data have no truncation at any angle. To reduce this bias, we propose to use the largest right singular vector (LRSV) of the system matrix as the initial condition, and demonstrate that the bias can be reduced with the LRSV. When data truncation is reduced, the LRSV approaches the FIC. This result does not contradict to the use of FIC when projection data are not truncated. We also demonstrate that the reconstructed transmission image using LRSV as initial condition provides a more accurate attenuation coefficient distribution than that using FIC. However, the improvement is mostly in the area outside the DSR.