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 threedimensional (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.
In the paper, we present a new hardware acceleration method to speedup the ordered-subsets expectation-maximization (OS-EM) algorithm for quantitative SPECT (single photon emission computed tomography) image reconstruction with varying focal-length fan-beam (VFF) collimation. By utilizing the geometrical symmetry of VFF point-spread function (PSF), compensation for object-specific attenuation and system-specific PSF are accelerated using currently available PC video/graphics card technologies. A ten-fold acceleration of quantitative SPECT reconstruction is achieved.
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.
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