Effect of errors in the system matrix on iterative image reconstruction

Statistically based iterative image reconstruction is widely used in emission tomography. One important component in iterative image reconstruction is the system matrix, which defines the mapping from the image space to the data space. Several groups have demonstrated that an accurate system matrix can improve image quality in both SPECT and PET. While iterative methods are amenable to arbitrary and complicated system models, the true system response is never known exactly. In practice, one also has to sacrifice the accuracy of the system model because of limited computing and imaging resources. This paper analyzes the effect of errors in the system matrix on iterative image reconstruction. We derived a theoretical expression for calculating artifacts in a reconstructed image that are caused by errors in the system matrix. Using this theoretical expression, we can address the question of how accurate the system matrix needs to be. Computer simulations were conducted to validate theoretical results.