A unified noise analysis for iterative image estimation

Iterative image estimation methods have been widely used in emission tomography. Accurate estimation of the uncertainty of the reconstructed images is essential for quantitative applications. While both iteration-based noise analysis and fixed-point noise analysis have been developed, current iteration-based results are limited to only a few algorithms that have an explicit multiplicative update equation and some may not converge to the fixed-point result. This paper presents a theoretical noise analysis that is applicable to a wide range of preconditioned gradient-type algorithms. Under a certain condition, the proposed method does not require an explicit expression of the preconditioner. By deriving the fixed-point expression from the iteration-based result, we show that the proposed iteration-based noise analysis is consistent with fixed-point analysis. Examples in emission tomography and transmission tomography are shown. The results are validated using Monte Carlo simulations.