SS3D-Fast fully 3D PET iterative reconstruction using stochastic sampling

We have developed a three-dimensional (3-D) reconstruction procedure for positron emission tomography (PET) using stochastic sampling techniques-the SS3D algorithm. A forward- and back-projector pair has been developed that eliminates the need to explicitly calculate the system response matrix (SRM). This is advantageous as it eliminates the memory requirements for storing this matrix. As compared to on-the-fly methods, our method is more accurate in its assumptions and can readily incorporate various physical effects of attenuation, scatter, and detector characteristics. This method can be efficiently used with "simultaneous" or "row action" algorithms like image space reconstruction algorithm (ISRA), expectation maximization (EM), and ordered subsets expectation maximization (OSEM). We demonstrate the successful implementation of this technique with the maximum likelihood expectation maximization (ML-EM), maximum a posteriori expectation maximization (MAP-EM), and maximum a posteriori ordered subsets expectation maximization (MAP-OS-EM) algorithms by evaluating the images on the basis of uniformity of noise, contrast recovery, signal-to-noise ratio (SNR), point-spread function, structural accuracy, and computational time.