Maximum likelihood algorithm for PET image reconstruction based on fuzzy random variable

This work presents a new iterative method for reconstructing positron emission tomography (PET) images. Unlike conventional maximum likelihood-expectation maximization (MLEM), this method intends to introduce the fuzzy set principle to MLEM algorithm. In this work, the noncognitive uncertainty of the observed projection data are described by their probability density function; whereas the cognitive uncertainty of a random variable can be described by the membership function for its fuzziness. The mean of the observed projection data are regard as fuzzy random variables because of the complexity of system. The fuzzy random variable can be represented by a triangular membership function. We establish a joint probability density function that includes the effects of both fuzziness and randomness. The maximum likelihood approach is used to estimate the image vector. The order subset (OS), rescaled block-iterative (RBI), and row-action (RA) techniques are applied to our PET reconstructed method to speed up the convergence rate and to decrease the iteration numbers.