Calculation of attenuation factors from combined singles and coincidence emission projections

We have developed a simple method for determining coincidence attenuation-correction factors C (the inverse of the total attenuation factors) from collimated singles (SPECT) and coincidence [positron emission tomography (PET)] projections without transmission data. Attenuation-correction factor estimates are determined for individual lines of response (LOR's) independently. The required data can be acquired using a gamma-camera system with coincidence capabilities. A first-order approximation (R) of C for an LOR is given by the product of the singles count rates, taken at each end of the LOR divided by the square of the coincidence count rate. The method was tested using simulated singles and coincidence projections starting with emission and attenuation maps from patient PET scans. Noise and resolution effects were modeled in separate studies. In the noise-free, high-resolution simulations, a scatter plot of the C values versus the corresponding R values for all LOR's produces a well-defined trajectory with little variance. Values of lnR were reconstructed into good quality attenuation maps that compare favorably with the originals. We conclude that the method works well on ideal data. The introduction of noise results in degraded images. In a simulated patient study, lung and outer body boundaries were visible in images produced with 3.2 x 10(4) coincidence counts.