A combined transformation of ordering SPECT sinograms for signal extraction from measurements of poisson noise

A theoretically based transformation, which reorders SPECT sinograms degraded by the Poisson noise according to their signal-to-noise ratio (SNR), has been proposed. The transformation is equivalent to the maximum noise fraction (MNF) approach developed for Gaussian noise treatment. It is a two-stage transformation. The first stage is the Anscombe transformation, which converts Poisson distributed variable into Gaussian distributed one with constant variance. The second one is the Karhunen-Loeve (K-L) transformation along the direction of the slices, which simplifies the complex task of three-dimensional (3D) filtering into 2D spatial process slice-by-slice. In the K-L domain, the noise property of constant variance remains for all components, while the SNR of each component decreases proportional to its eigenvalue, providing a measure for the significance of each components. The availability of the noise covariance matrix in this method eliminates the difficulty of separating noise from signal. Thus we can construct an accurate 2D Wiener filter for each sinogram component in the K-L domain, and design a weighting window to make the filter adaptive to the SNR of each component, leading to an improved restoration of SPECT sinograms. Experimental results demonstrate that the proposed method provides a better noise reduction without sacrifice of resolution.