Propagation of errors from the sensitivity image in list mode reconstruction

List mode image reconstruction is attracting renewed attention. It eliminates the storage of empty sinogram bins. However, a single back projection of all LORs is still necessary for the pre-calculation of a sensitivity image. Since the detection sensitivity is dependent on the object attenuation and detector efficiency, it must be computed for each study. Exact computation of the sensitivity image can be a daunting task for modern scanners with huge numbers of LORs. Thus, some fast approximate calculation may be desirable. In this paper, we theoretically analyze the error propagation from the sensitivity image into the reconstructed image. The theoretical analysis is based on the fixed point condition of the list mode reconstruction. The non-negativity constraint is modeled using the Kuhn-Tucker condition. With certain assumptions and the first order Taylor series approximation, we derive a closed form expression for the error in the reconstructed image as a function of the error in the sensitivity image. The result provides insights on what kind of error might be allowable in the sensitivity image. Computer simulations show that the theoretical results are in good agreement with the measured results.