In single photon emission computed tomography (SPECT), the Poisson noise in sinogram data is one of the major degrading factors that jeopardize the quality of reconstructed images. The common strategy to reduce noise in SPECT images is to apply low-pass pre- or post-processing filters, which suppress the noise by attenuating the high frequency components that can contain valuable edge/detail information. In the past years, the statistical sinogram restoration approaches have shown great potential to suppress the noise without noticeable sacrifice of the spatial resolution for low-dose X-ray CT. Therefore, in this work, we tried to extend them to noise reduction for SPECT imaging. With the Poisson noise model, two well-known statistical criteria, penalized maximum-likelihood (PML) and penalized weighted least-squares (PWLS), were derived for SPECT sinogram restoration. A quadratic form penalty with edge-preserving anisotropic weights was adopted in this study, and the Gauss-Seidel update algorithm was employed to optimize the two criteria. We validated their feasibility and effectiveness on SPECT sinogram smoothing under both low and high noise level with a digital thorax phantom.