A new approach to estimate the 2D-PSF in SPECT

Abstract

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Objectives: Corruption of scattered photons in the projections is one of the image degradations in SPECT. Many scatter compensation methods have been investigated. An accurate scatter model is important for the scatter compensation. A popular model is the scatter point response functions in the projection data. In our previous research, we proposed a new model to estimate the scattering with a two dimensional point spread function (2D-PSF) in the reconstructed image. In this study, we explore a revised method to obtain the 2D-PSF. Methods: The 2D-PSF is defined as the reconstructed image of the point source blurred projections with attenuation compensation. We model this 2D-PSF as a Gaussian function with only five variables: the magnitude A0, the full-width at half-maximum on the major axis FWHMl, the full-width at half-maximum in the minor axis FWHMs, and the center (x0,y0). The magnitude A0 for a certain point source is derived as a function of the distance from this point source to the center of the image. The FWHMl and FWHMs are determined by the combination effects of the collimator blurring and the scatter blurring. The latter is proportional to the energy window in the camera. The center of the Gaussian function is simply the location of the point source. In this way, we are able to estimate the 2D-PSF with only an attenuation map and the collimator parameters. Results: The 2D-PSF for a point source at different locations in homogeneous scatter medium was obtained using our proposed method. The 2D-PSF obtained using Monte Carlo approach was also implemented as a standard to validate our method. The parallel hole collimator was modeled with a thickness of 2cm and hole diameter of 0.14cm. The detection energy window was centered at 140keV with a width of 10%. The experimental results show fairly good agreement between our proposed method and the Monte Carlo approach. Conclusions: We presented a new way to estimate the 2D-PSF in the image domain. The 2D-PSF is obtained efficiently using only the attenuation map and collimator parameters. Our method works for both uniformly and non-uniformly attenuated phantom even though only the uniform case is studied at this point. More research needs to be done for more realistic phantoms. This 2D-PSF can be used to compensate for the scattering effect and deblur the image, as a post-processing method.