Properties of edge artifacts in PSF-based PET reconstruction

PSF (point spread function) based image reconstruction causes an overshoot at sharp intensity transitions (edges) of the object. This edge artifact, or ringing, has not been fully studied. In this work, we analyze the properties of edge artifacts in PSF-based reconstruction in an effort to develop mitigation methods. Our study is based on 1D and 2D noise-free simulation experiments. Two approaches are adopted to analyze the artifacts. In the system theory approach, we relate the presence of edge artifacts to the null space and conditioning of the imaging operator. We show that edges can not be accurately recovered with a practical number of image updates when the imaging matrices are poorly conditioned. In the frequency-domain analysis approach, we calculate the object-specific modulation transfer function (OMTF) of the system, defined as spectrum of the reconstruction divided by spectrum of the object. We observe an amplified frequency band in the OMTF of PSF-based reconstruction, and this band is directly related to the presence of ringing. Further analysis shows the amplified band is linearly related to kernel frequency support, and the relation holds for different objects. These results are helpful to determine mitigation methods for edge artifacts.