title: A unified noise analysis for iterative image estimation.
abstract: 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.
authors.affiliation: Department of Nuclear Medicine and Functional Imaging, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA. jqi@lbl.gov
authors.forename: Jinyi
authors.initials: J
authors.lastname: Qi
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D005246:Feedback; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D008954:Models, Biological; D015233:Models, Statistical; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D013269:Stochastic Processes; D014055:Tomography, Emission-Computed / Q000379:methods*; D015899:Tomography, Emission-Computed, Single-Photon / Q000379:methods