Thomas H. Farquhar

High-resolution 3D Bayesian image reconstruction using the microPET small-animal scanner

A Bayesian method is described for reconstruction of high-resolution 3D images from the microPET small-animal scanner. Resolution recovery is achieved by explicitly modelling the depth dependent geometric sensitivity for each voxel in combination with an accurate detector response model that includes factors due to photon pair non-collinearity and inter-crystal scatter and penetration. To reduce storage and computational costs we use a factored matrix in which the detector response is modelled using a sinogram blurring kernel. Maximum a posteriori (MAP) images are reconstructed using this model in combination with a Poisson likelihood function and a Gibbs prior on the image. Reconstructions obtained from point source data using the accurate system model demonstrate a potential for near-isotropic FWHM resolution of approximately 1.2 mm at the center of the field of view compared with approximately 2 mm when using an analytic 3D reprojection (3DRP) method with a ramp filter. These results also show the ability of the accurate system model to compensate for resolution loss due to crystal penetration producing nearly constant radial FWHM resolution of 1 mm out to a 4 mm radius. Studies with a point source in a uniform cylinder indicate that as the resolution of the image is reduced to control noise propagation the resolution obtained using the accurate system model is superior to that obtained using 3DRP at matched background noise levels. Additional studies using pie phantoms with hot and cold cylinders of diameter 1-2.5 mm and 18FDG animal studies appear to confirm this observation.

Fully 3D Bayesian image reconstruction for the ECAT EXACT HR

A fully 3D Bayesian method is described for high resolution reconstruction of images from the Siemens/CTI ECAT EXACT HR+ whole body positron emission tomography (PET) scanner. To maximize resolution recovery from the system the authors model depth dependent geometric efficiency, intrinsic detector efficiency, photon pair non-colinearity, crystal penetration and inter-crystal scatter. They also explicitly model the effects of axial rebinning and angular mashing on the detection probability or system matrix. By fully exploiting sinogram symmetries and using a factored system matrix and automated indexing schemes, the authors are able to achieve substantial savings in both the storage size and time required to compute forward and backward projections. Reconstruction times are further reduced using multi-threaded programming on a four processor Unix server. Bayesian reconstructions are computed using a Huber prior and a shifted-Poisson likelihood model that accounts for the effects of randoms subtraction and scatter. Reconstructions of phantom data show that the 3D Bayesian method can achieve improved FWHM resolution and contrast recovery ratios at matched background noise levels compared to both the 3D reprojection method and an OSEM method based on the shifted-Poisson model.

Techniques to improve the spatial sampling of MicroPET-a high resolution animal PET tomograph

A method is described to improve the spatial sampling of microPET, a high resolution PET scanner designed for imaging small laboratory animals. The high intrinsic resolution of the microPET detector (1.58 mm FWHM), in combination with the stationary ring geometry of the tomograph, generate an imaging system which is inherently spatially undersampled. As a result the imaging resolution measured with a three-dimensional (3-D) filtered backprojection (FBP) algorithm for a point source at the center of the field of view (CFOV) is only 1.8 mm FWHM and has large fluctuations at positions near the CFOV. A small wobble motion was introduced via a circular motion of the scanner bed in the transverse plane, with a wobble radius of 300 /spl mu/m. The data was acquired with a step-and-shoot method by dividing the wobble circle into a number of equidistantly sampled intervals. The separate sinograms were interpolated to a finely resampled sinogram, which was reconstructed with the 3-D filtered backprojection algorithm. The resulting images demonstrated full recovery of the intrinsic detector resolution and elimination of the local nonuniformities of the point spread function (PSF) at the CFOV, with three wobble samples. The resulting average resolution improvement fur the central 5 cm of the FOV was approximately 13% in the radial and 19% in the tangential direction, with an associated 50% penalty in the reconstructed image noise.

Investigation of accelerated Monte Carlo techniques for PET simulation and 3-D PET scatter correction

The authors have been developing Monte Carlo Techniques for calculating primary and scatter photon distributions in PET. Their first goal has been to accelerate the Monte Carlo Code for fast PET simulation. Their second goal has been to use the simulation to analyze scatter effects in PET and explore the potential for use in scatter correction of clinical 3D PET studies. The authors have reduced the execution time to about 30 minutes or /spl sim/1 million coincidences per minute on a dual 300 MHz processor UltraSparcII workstation. The short execution time makes it feasible to use this technique for 3D PET scatter correction in the clinic. Fast simulation also allows the authors rapid feedback for the close examination of the accuracy of the method. They present techniques used to improve computational efficiency of Monte Carlo PET simulations. They use the simulation to analyze how scatter from within the body, outside the FOV, and from scanner shielding as well as the chosen energy threshold affect 3D PET sinograms.

An investigation of filter choice for filtered back-projection reconstruction in PET

A key parameter in the practical application of filtered back-projection (FBP), the standard clinical image reconstruction algorithm for positron emission tomography (PET), is the choice of a low-pass filter window function and its cut-off frequency. However, the filter windows and cut-off frequencies for clinical reconstruction are usually chosen empirically, based on a small sample of images and filters. By considering the features of the signal and noise spectra in a sinogram, the desired image resolution, and the signal-to-noise ratio (SNR) of the filtered sinogram, the authors investigated the possibility of establishing a methodology for informed selection of a filter function and cut-off frequency for use with FBP. Simulations of sinogram data similar to whole body or cardiac studies provided information on the signal and noise frequency-domain spectrum of noisy projection data. The improvements in the SNR with different filter windows and cut-off frequencies were evaluated and compared. The projection spectrum SNR measure did not prove to be an accurate indicator of subjective image quality or lesion detectability with variations in Poisson noise and image resolution.

An evaluation of exact and approximate 3-D reconstruction algorithms for a high-resolution, small-animal PET scanner

MicroPET is a low-cost, high resolution positron emission tomography (PET) scanner designed for imaging small animals. MicroPET operates exclusively without septa, acquiring fully three-dimensional (3-D) data sets. The performance of the projection-reprojection (3DRP), variable axial rebinning (VARB), single slice rebinning (SSRB), and Fourier rebinning (FORE) methods for reconstruction of microPET data were evaluated. The algorithms were compared with respect to resolution, noise variance, and reconstruction time. Results suggested that the 3DRP algorithm gives the best combination of resolution and noise performance in 9 min of reconstruction time on a Sun UltraSparc I workstation. The FORE algorithm provided the most acceptable accelerated method of reconstruction, giving similar resolution performance with a 10%-20% degradation in noise variance in under 2 min. Significant degradation in the axial resolution was measured with the VARB and SSRB methods, offsetting the decrease in reconstruction time achieved with those methods. In-plane angular mashing of the 3-D data before reconstruction led to a 50% reduction in reconstruction time but also introduced unacceptable tangential blurring artifacts. This thorough evaluation of analytical 3-D reconstruction techniques allowed for optimal selection of a reconstruction method for the diverse range of microPET applications.

Removal of the effect of Compton scattering in 3-D whole body positron emission tomography by Monte Carlo

A Monte Carlo technique has been developed to simulate and correct for the effect of Compton scatter in 3-D acquired PET whole body imaging. The method utilizes the attenuation corrected and normalized, 3-D reconstructed image volume as the source intensity distribution for a photon-tracking Monte Carlo simulation. It is assumed that the number of events in each pixel of the image represents the isotope concentration at that location in the body. The history of each annihilation photons interactions in the scattering media is followed. The edges and average attenuation coefficients of the various scattering media are determined using a segmented image volume derived from a short transmission scan. The sinograms for the scattered and unscattered photon pairs are generated in a simulated 3-D PET acquisition. The calculated scatter contribution is used to correct the original data set. The method is general and can be applied to any scanner configuration or geometry. In its current form the simulation requires 20 hours on a Sparc10 when every pixel in a 89-plane, 128/spl times/128 pixel, 3-D acquired (CTI 961, two bed positions) image volume is sampled, and roughly 1 hour when 16 pixels (4/spl times/4) are grouped as a single pixel. Here, the authors present results of the scatter correction method using a 3-D acquired human study of the thorax as input.

A nonlinear, image domain filtering method for PET images

An adaptive, nonlinear image domain filtering strategy is described which improves positron emission tomography (PET) images. The method was formulated to improve on the linear, low-pass filtering typically applied to each projection in the filtered back-projection (FBP) reconstruction algorithm. The algorithm is a potential alternative to linear smoothing which reduces noise but degrades resolution; this method uses the FBP algorithm for reconstruction, but aims to incorporate some of the statistical information and nonlinear smoothing utilized in iterative reconstruction algorithms. The approach uses sinogram segmentation to separate the sinogram elements with higher and lower signal-to-noise ratios, and then reconstruct each with FBP using a more appropriate choice of filter and cut-off frequency. Also, this algorithm addresses the radial streak artifacts introduced by FBP. The algorithm was evaluated using simulations as well as clinical data of cardiac PET studies on an ECAT 931 PET scanner. The initial results suggest that this technique has advantages over the current clinical protocol. Images processed with the method show generally improved visual image quality and reduced radial streaks without the introduction of artifacts. Also, by using a higher resolution filter for the high activity segment of the sinogram, increased contrast recovery and resolution are realized.

A nonlinear, image domain filtering method for cardiac PET images

An adaptive, nonlinear image domain filtering strategy is described which improves positron emission tomography (PET) images. The method was formulated to improve on the linear, low-pass filtering typically applied to each projection in the filtered back-projection (FBP) reconstruction algorithm. The algorithm is a potential alternative to linear smoothing which reduces noise but degrades resolution; this method uses the FBP algorithm for reconstruction, but aims to incorporate some of the statistical information and nonlinear smoothing utilized in iterative reconstruction algorithms. The approach uses sinogram segmentation to separate the sinogram elements with higher and lower signal-to-noise ratios, and then reconstruct each with FBP using a more appropriate choice of filter and cut-off frequency. Also, this algorithm addresses the radial streak artifacts introduced by FBP. The algorithm was evaluated using simulations clinical data of cardiac PET studies on an ECAT 931 PET scanner. The initial results suggest that this technique has advantages over the current clinical protocol. Images processed with the method show generally improved visual image quality and reduced radial streaks without the introduction of artifacts. In simulations, increased contrast recovery and resolution are realized without an increase in the background noise of the reconstructed images.