Image reconstruction method

The image reconstruction method uses the MLEM algorithm as the iterative image reconstruction technique. The MLEM is based on the log-maximization of the Poisson-like probability function and described in the following equation¹⁵:

where y contains the measured mask projection, in which y_i is the number of counts recorded by detector pixel i. That is, a point source is present in the projection because the projection of the source through the mask is deposited on the detector. A is the system matrix consisting of the estimated mask projections from various source positions, where A_ij is the predicted response of detector pixel i when the source is located in source-plane pixel j. If there is a mismatch between the measured and estimated projection (λ_k, the ratio of two sets of projection), modifications are made to improve the estimate, and a new iteration is performed until k, the maximum iteration counter, is reached. This process leads to the maximized probability (λ_j) when the source is located at a source plane pixel j. The term b is a noise term that represents the probability derived from the background radiation. Therefore, this process can readily estimate the position of the radiation source with a small number of incident radiation enough to form the mask projection. This procedure was implemented in MATLAB (MathWorks Inc, USA).