A noise reduction method for non-stationary noise model of SPECT sinogram based on Kalman filter

The non-stationary Poisson noise in single photon emission computed tomography (SPECT) sinogram is a major cause to compromise the quality of reconstructed images and challenge any compensation strategy for photon attenuation, scatter and collimator response. Research utilizing three-dimensional Wiener filter after Anscombe transformation, which converts Poisson distributed noise into Gaussian distributed one, has been conducted recently with noticeable success. However, the prerequisite of stationary random process for the Wiener approach is not exactly valid for the SPECT sinogram. In this paper, the non-stationary Poisson noise was first modulated by the Anscombe transformation and then the modulated noise model was analyzed. A Kalman filter for the modulated non-stationary noise model was designed to extract the means or signals from the Poisson noise sinogram. Monte Carlo program was used to generate projection data from the MCAT phantom, simulating SPECT data acquisition. The reconstructed results demonstrated a significant improvement with the Kalman filter, as compared to the Wiener approach. Dramatic improvement is seen, as compared to linear low-pass filters, at noisy levels of 100 thousand counts in a 128×128×128 sinogram size. The capability of Kalman filter for non-stationary noise model was theoretically proved and experimentally demonstrated.