Application of the noise power spectrum to positron emission CT self-absorption correction

Two methods are compared in correcting for self-absorption in positron emission CT scans, or equivalently, in determining the integral of attenuation along a strip in a cross section. These are CT reconstruction and direct measurement. It is shown that the former method is slightly more precise than the latter with the degree of improvement proportional to the number of angles used. Additionally, it is demonstrated that the CT approach is statistically very inefficient in its use of detected events in comparison to the direct approach. For the CT case, it is shown using the noise power spectrum that two-thirds of the variance in the attenuation integral is from one projection alone, namely that along the direction of the strip. The remaining one-third is primarily from adjacent projections. For the problem of determining the attenuation in a single strip within the slice, the CT approach is not recommended. However, if the problem is extended to a complete set of strips within the slice, as is desired in positron emission CT, the CT approach may require considerably less counting time than the direct approach for comparable precision.