A three-dimensional iterative reconstruction algorithm which incorporates models of the geometric point response in the projector-backprojector is presented for parallel, fan, and cone beam geometries. The algorithms have been tested on an IBM 3090-600S supercomputer. The iterative EM reconstruction algorithm is 50 times longer with geometric response and photon attenuation models than without modeling these physical effects. An improvement in image quality in the reconstruction of projection data collected from a single-photon-emission computed tomography (SPECT) imaging system has been observed. Significant improvements in image quality are obtained when the geometric point response and attenuation are appropriately compensated. It is observed that resolution is significantly improved with attenuation correction alone. Using phantom experiments, it is observed that the modeling of the spatial system response imposes a smoothing without loss of resolution. >

Three-dimensional iterative reconstruction algorithms with attenuation and geometric point response correction

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 correction for spatially variant collimator blurring in SPECT

Geometric response functions are derived for both cone and fan beam collimators for the scintillation camera. The formulation is based on an effective response function which is determined by the geometric response of a single hole. The technique provides an accurate description of the spatial resolution by characterising the complete geometric response function which includes the effects of the shape and orientation of the collimator holes. The theoretical formulation was used to design a fan beam collimator for SPECT imaging and was shown to agree well with the experimental results.

https://iopscience.iop.org/article/10.1088/0031-9155/35/1/008/pdf

The geometric transfer function for cone and fan beam collimators

Three procedures for the removal of Compton-scattered data in SPECT by constrained deconvolution are presented. The first is a deconvolution of a 2-D measured PSRF containing scatter from a single reconstructed transaxial image; the second is a deconvolution of a 2-D measured point-source response function (PSRF) from each frame of projection data prior to reconstruction; the third involves deconvolution of a 3-D measured PSRF from a stack of reconstructed slices. Results of applying these procedures to data obtained from a phantom containing cold cylinders and to data from a cold spot-resolution phantom are presented and are shown to be superior to the results of correcting for scatter by scatter-window substraction. Both 3-D deconvolution from reconstructed images and 2-D deconvolution from projection data show major improvements in image contrast, resolution, and quantitation. Improvements are especially marked for small (1.0-3.0 cm) cold sources. >

A comparison of deconvolution and windowed subtraction techniques for scatter compensation in SPECT

A complete theory of camera multihole collimators is presented. The geometrical system response is determined in closed form in frequency space. This closed form accounts for the known efficiency and resolution formulae for parallel beam, fan beam, cone beam and astigmatic collimators as well as for the most frequent hole array patterns and hole shapes. The point spread function in the space domain for a certain collimator and source position can be calculated via a discrete fast Fourier transform. Beside the complete theoretical definition of the response of multihole collimators, this theory allows the definition of accurate models of the geometrical response for SPECT reconstruction and it is suitable for designing new collimators.

http://iopscience.iop.org/article/10.1088/0031-9155/43/11/013/pdf

Geometrical response of multihole collimators

A new technique for evaluating the point spread function of parallel hole collimators in scintillation cameras is studied. The collimator function is developed into a Fourier series and the intensity distribution in the detector plane for a point source is given by a mathematical expression that depends on the object position and on the collimator parameters. The septal penetration effect is considered. The technique is applied to obtain the general formulae for collimators with hexagonal holes and the PSF is evaluated.

http://iopscience.iop.org/article/10.1088/0031-9155/24/2/013/pdf

A study of the point spread function in scintillation camera collimators based on Fourier analysis.

A method to study the relative influences of the collimator and the detector on the final image of a scintillation camera is proposed. The collimator response is studied by applying a technique based on the Fourier analysis for evaluating the point spread function (PSF) of parallel holes collimators. A mathematical expression for the PSF is obtained and from it the collimator MTF and plane sensitivity are evaluated. The scintillation camera response is obtained from the LSF measured experimentally. The detector response is obtained from these results. The method is applied to a Toshiba GCA 102 scintillation camera and from the results obtained the relative influences of the collimator and the detector on the image deterioration as a function of the object distance are discussed.

S. Miracle

Papers

A study of the point spread function in scintillation camera collimators based on Fourier analysis.

Evaluation and Comparison Between the Collimator and the Detector Responses in a Scintillation Camera