Random-coincidence corrections using iterative reconstruction for PET images

Iterative reconstruction (IR) algorithms can reduce artifacts caused by filtered backprojection (FBP) or convolution backprojection (CBP). Recently, the computational effects required for IR of positron emission tomography (PET) studies have been reduced to make it practically appealing. We have made an implementation of the improved Maximum Likelihood-Expectation Maximization (ML-EM) algorithm. The transition matrix was generated based on the geometry of the instrument. Phantoms of 6 line sources and 19 line sources were used to test our accelerated ML-EM algorithms against the FBP method. The singles were used to calculate the random coincidence rates by a well known formula and were compared to the randoms obtained by another geometric method. We also designed a new model using two line sources to determine the ratio of random events to true events. The artifacts near those line sources were eliminated with the ML-EM method. With decay correction, the RC events were uniformly distributed in whole field after 10 iterations. The ML-EM reconstructed images are superior to those obtained with FBP. The patterns of randoms provide insightful information for random correction, which the hardware correction by the delay window can not provide. This information is particular valuable when the delay window correction is not available in the old fashion PET scanner.