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A unified noise analysis for iterative image estimation

Abstract

Iterative image estimation methods have been widely used in emission tomography. Accurate estimate of the uncertainty of the reconstructed images is essential for quantitative applications. While theoretical approach has been developed to analyze the noise propagation from iteration to iteration, the current results are limited to only a few iterative algorithms that have an explicit multiplicative update equation. This paper presents a theoretical noise analysis that is applicable to a wide range of preconditioned gradient type algorithms. One advantage is that proposed method does not require an explicit expression of the preconditioner and hence it is applicable to some algorithms that involve line searches. By deriving fixed point expression from the iteration based results, we show that the iteration based noise analysis is consistent with the xed point based analysis. Examples in emission tomography and transmission tomography are shown.

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