Fourier correction for spatially variant collimator blurring in SPECT

Abstract

In single-photon emission computed tomography (SPECT), projection data are acquired by rotating the photon detector around a patient, either in a circular orbit or in a noncircular orbit. The projection data of the desired spatial distribution of emission activity is blurred by the point-response function of the collimator that is used to define the range of directions of gamma-ray photons reaching the detector. The point-response function of the collimator is not spatially stationary, but depends on the distance from the collimator to the point. Conventional methods for deblurring collimator projection data are based on approximating the actual distance-dependent point-response function by a spatially invariant blurring function, so that deconvolution methods can be applied independently to the data at each angle of view. A method is described here for distance-dependent preprocessing of SPECT projection data prior to image reconstruction. Based on the special distance-dependent characteristics of the Fourier coefficients of the sinogram, a spatially variant inverse filter can be developed to process the projection data in all views simultaneously. The algorithm is first derived from Fourier analysis of the projection data from the circular orbit geometry. For circular orbit projection data, experimental results from both simulated data and real phantom data indicate the potential of this method. It is shown that the spatial filtering method can be extended to the projection data from the noncircular orbit geometry. Experiments on simulated projection data from an elliptical orbit demonstrate correction of the spatially variant blurring and distortion in the reconstructed image caused by the noncircular orbit geometry.

Fourier properties of the fan-beam sinogram

“…They have also been used to improve computational efficiency in 3D reconstruction. Examples can be found in x-ray CT, 3-9 PET, [10][11][12][13][14][15][16][17] SPECT, [18][19][20][21][22][23][24] and MRI. 25 For parallel beam sinograms, Rattey 26 and, later, Edholm 1 derived that the 2D Fourier transform of the sinogram has an empty "double-wedge" region whose boundary slope is proportional to the radial extent of the object.…”

Novel Multiple-Channel Polycrystalline Silicon Thin-Film Transistors Employing Asymmetric Spacing

“…The EPSF can be useful in collimator-response compensation in both analytic and iterative image reconstruction algorithms (Tsui et al 1988, Xia et al 1995, Formiconi et al 1989, Frey and Tsui 2006. Based on the EPSF, we derived sensitivity and spatial resolution formulae for SS collimation.…”

Sinogram bow‐tie filtering in FBP PET reconstruction

“…11͒ and to compensate for spatially variant collimator blurring in single photon emission computed tomography. 12 Also, Andía 13 exploited this property to develop optimal nonstationary linear filters based on sinogram statistics.…”