A unified noise analysis for iterative image estimation.

Jinyi Qi

doi:10.1088/0031-9155/48/21/004

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A unified noise analysis for iterative image estimation.

Jinyi Qi

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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.

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Algorithms Computer Simulation Feedback Image Enhancement Image Interpretation, Computer-Assisted Models, Biological Models, Statistical Reproducibility of Results Sensitivity and Specificity Stochastic Processes Tomography, Emission-Computed Tomography, Emission-Computed, Single-Photon Comparative Study Evaluation Study Journal Article Research Support, U.S. Gov't, Non-P.H.S.Research Support, U.S. Gov't, P.H.S.Validation Study

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Jinyi Qi. 2003-11-07. A unified noise analysis for iterative image estimation.. https://doi.org/10.1088/0031-9155%2F48%2F21%2F004

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