A theoretically based pre-reconstructing filter for spatio-temporal noise reduction in gated cardiac SPECT

In dynamic SPECT studies, the acquired sinograms have both spatial and temporal correlations among the time sequence, in addition to the spatial correlation within each time frame (i.e., a three-dimensional (3D) sinogram). In this paper, we propose a theoretically based multi-frame filtering algorithm, which considers both the spatial and temporal correlations, for restoring the gated sinograms degraded by the Poisson noise. This spatio-temporal filtering task is greatly simplified by first applying the Anscombe transformation to all the sinogram data, which converts Poisson distributed noise into Gaussian distributed one with constant variance (i.e., the noise is signal independence). By performing temporal Karhune-Loeve (K-L) transformation on the Anscombe transformed data sequence, the filtering task is further simplified from a 4D problem to a 3D spatial process. In the K-L domain, the noise property of constant variance remains for all components, while the signal-to-noise ratio decreases monotonically for lower eigenvalue components. An accurate Wiener filter is then constructed for each component of a 3D data set. By this approach, the spatio-temporal filtering can be achieved at a reasonable computational cost. The computer simulations are very encouraging, by visual judgement, as compared to frame-by-frame 3D Wiener filtering along the time sequence.