Stochastic Discrete Reconstruction (SDR) for Nuclear Medicine Tomographic Systems

To address the challenge posted by novel tomographic systems we have designed a stochastic reconstruction method. Our algorithm considers every event separately, therefore the method is ideally suited and designed for reconstruction of data from imaging systems with a large number of line of responses (LORs) that usually yield up to only one event per LORs. SDR is also entirely compatible with reconstruction of unusual geometries such as for time of flight positron emission tomography (TOF-PET) or Compton aperture imaging. The main idea behind the SDR is to find in the reconstruction area the origin of each of the detected events. In every iteration of the algorithm, the possible origin of each event is changed stochastically according to some predefined transition probability. The reconstruction is considered completed when the system reaches equilibrium. Then, the activity in each voxel is estimated by the current number of events in the voxel normalized by the sensitivity of the system. This approach does not require either projection or backprojection operations as would be the case for standard iterative algorithms. We tested the performance of the new method using 2D computer simulations of standard tomographic parallel geometry. For the reconstructions with a high level of noise, the bias and variance obtained by the SDR reconstructions was in the range of 5-10% which was comparable to the results obtained by maximum likelihood expectation maximization (ML-EM).