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.
ASJC Scopus subject areas
- Biomedical Engineering
- Physics and Astronomy (miscellaneous)
- Radiology Nuclear Medicine and imaging
- Radiological and Ultrasound Technology