A 3D distance-weighted Wiener filter for poisson noise reduction in sinogram space for SPECT imaging

A three-dimensional (3D) distance-weighted Wiener filtering, which takes the characteristics of Poisson noise into account as well as the frequency-distance relationship of projection data, is described and evaluated. The task of spatial filtering on Poisson noise can be greatly simplified without the estimation of noise-power spectrum by first applying the Anscombe transformation to the projection data, which converts Poisson distributed noise into Gaussian distributed one with constant variance. By extending the stationary-phase condition and frequency-distance relationship (derived from the noise-free 2D sinogram) into 3D situation, we obtain a weighting function in frequency domain which is only dependent on the distance of an interested point source from the object center. Since the Anscombe transformation only changes the distribution of projection data, not the pixel location, a distance-variant weighting window for the Anscombe transformed data is derived and incorporated into the Wiener filter. Considering the regions with higher signal-to-noise ratio (SNR) receive greater weight in the estimation of signal-power spectrum, the proposed filter optimizes the data used to estimate the power spectrum of observed data and thus produces a better spatial resolution. Simulation and experimental results show improved noise reduction, especially in the peripheral regions, as compared with conventional filtering methods.