Image reconstruction for a 3D PET system using a minimum norm constraint

Attenuation correction for three-dimensional PET using uncollimated flood-source transmission measurements

An attenuation-correction method for three-dimensional PET imaging, which obtains attenuation-correction factors from transmission measurements using an uncollimated flood source, is described. This correction is demonstrated for two different phantoms using transmission data acquired with QPET, a rotating imaging system with two planar detectors developed for imaging small volumes. The scatter amplitude in the transmission projections was a maximum of 30%; to obtain accurate attenuation-correction factors the scatter distribution was first calculated and subtracted. The attenuation-corrected emission images for both phantoms indicate that their original uniform amplitudes have been restored. The attenuation correction adds only a small amount of noise to the emission images, as evaluated from the standard deviation over a central region. For the first phantom, with maximum attenuation of 48%, the noise added was 2.6%. The second phantom was attenuated by a maximum of 37%, and 1.9% noise was added. Because the transmission data are smoothed, some artifacts are visible at the edges of the phantom where the correction factors change abruptly within the emission image.

Scatter correction for three-dimensional PET based on an analytic model dependent on source and attenuating object

Three-dimensional positron emission tomography admits a significant scatter fraction due to the large aperture of the detectors, and requires accurate scatter subtraction. A scatter-correction method, applicable to both emission and transmission imaging, calculates the projections of the single-scatter distribution, using an approximate image of the source and attenuating object. The scatter background is subtracted in projection space for transmission data and in image space for emission data, yielding corrected attenuation and emission images. The accuracy of this single-scatter distribution is validated for the authors' small imaging system by comparison with Monte Carlo simulations. The correction is demonstrated using transmission and emission data obtained from measurements on the authors' QPET imaging system using two acrylic phantoms. For the transmission data, generated with a flood source, errors of up to 24% in the linear attenuation coefficients resulted with no scatter subtraction, but the correction yielded an accurate value of mu =0.11+or-0.01 cm-1. For the emission data, the corrected images show that the scattered background has been removed to within the level of the background noise outside the source. The residual amplitude within a cold spot in one of the phantoms was reduced from 21% to 3% of the image amplitude.

Performance of QPET, a high-resolution 3D PET imaging system for small volumes

QPET is a positron imaging system developed at Queen's University for high-resolution, 3D imaging of small volumes; it includes a pair of planar gamma-ray detectors 25.4 cm square, which rotate about a central axis with a quasi-cylindrical geometry. The authors describe the performance of this system. Basic characteristics of the detectors are evaluated: a spatial sampling of 1 mm, a quantum efficiency of 9.3% (for 511 keV gamma rays with normal incidence), and a time resolution of 88 ns. Models are developed to characterize the system deadtime and the sensitivity in terms of the noise-equivalent counting rate. With an 8 cm diameter spherical source, the noise-equivalent counting rate reaches a maximum at just over 3 kcps for an activity concentration of 2 muCi/cc; the random coincidence events and the deadtime losses both contribute significantly and the scatter contribution is small. Spatial resolution and uniformity over the field of view are evaluated by imaging short and long line sources; a spatial resolution of 2.7 mm in the transverse directions and 2.0 mm in the axial direction is achieved, with excellent uniformity throughout the field of view. The detector response is amplitude invariant across a 20 cm transverse diameter and a 9 cm axial length with the acceptance angle limited to +/-25 degrees in the axial direction. As an example of the imaging capabilities of QPET, the authors show 3D images of (18)F uptake in the bones of a rat, showing the excellent spatial resolution. This system is best suited to limited-volume applications where high counting rates are not necessary, but where high spatial resolution and uniform detector response are priorities.

Signal-to-noise ratios for attenuation correction in PET imaging

Attenuation correction is an important part of accurate image reconstruction in positron tomography. The usual correction method involves direct measurement of attenuation correction factors (ACFs). A reconstruct-reproject method, which has been suggested as providing superior noise properties, is sometimes employed; an attenuation image is first reconstructed from the measurement and then ACFs are obtained by reprojection through this image. Here the authors present a model which follows the signal-to-noise ratio (SNR) through the attenuation correction by both the direct and reconstruct-reproject methods. This model is applicable to both 2D and 3D imaging geometry, but applies to the central elements of emission and transmission objects with circular symmetry and constant amplitude. For this simplified geometry, the model predicts that the SNR of the emission image following attenuation correction is the same for both direct and reconstruct-reproject methods, although the SNRs of the ACFs are themselves substantially different. The authors also present the measured SNR at the various steps of attenuation correction for both the direct and reconstruct-reproject methods using simulated transmission and emission data. The measured SNRs agree with the model; no significant difference between the direct and reconstruct-reproject SNRs was observed.

Removing the interference error between attenuation correction and scatter subtraction in 3D PET imaging

A method to remove the interference between attenuation correction and scatter subtraction has been developed for the QPET 3D imaging system at Queen's University. Because the detector system has more than 10(10) lines of response, we reconstruct the image by first backprojecting, then filtering. We correct for attenuation at backprojection by weighting each event by the inverse of the attenuation factor calculated by reprojection through an attenuation image. Since the scatter background has not been corrected at backprojection time, this has the side effect that a fraction of the detected scattered events get incorrectly weighted. When a scatter subtraction is subsequently applied, the correction is inaccurate because the scatter distribution has been modified by the attenuation correction procedure. The residual interference error in the reconstructed image is a distorted image of the attenuator. An approximation to this error is obtained by reprojecting through the attenuation image, backprojecting with appropriate weights, then reconstructing. This image is then scaled and multiplied by the calculated scatter distribution to obtain an estimate of the interference error. Both simulations and measurements indicate that for our system, this method provides a reasonable approximation of the interference error in the image.

A deconvolution scatter correction for a 3-D PET system

A method to remove the scattered background from a reconstructed image by deconvolution with a point response function which includes the scatter contribution is presented. The amplitude of the scattered response function is obtained by constraining a region of the corrected image to zero average amplitude. This method assumes that the shape of scatter distribution is shift invariant and independent of the shape of the scattering object and the distribution of the positron activity. The validity of these approximations for the QPET geometry was tested using simulations. An average scatter response function for the system was obtained from these simulations and compared with results from measurements. The method was tested using experimental data from an irregularly shaped acrylic phantom. It was simple to implement and resulted in a satisfactory correction of the scattered background for a small-volume system.

Accurate attenuation correction for a 3D PET system

An accurate attenuation correction has been developed for a small-volume three-dimensional positron emission tomography (PET) system. Transmission data were measured as twenty-four 2D slices which were reconstructed and combined to form a 3D attenuation image. Emission data were reconstructed using a backproject-then-filter technique, and each event was corrected for attenuation at backprojection time by a reprojection through the attenuation image. This correction restores the spatial invariance of the point response function, thus allowing a valid deconvolution and producing an undistorted emission image. Scattering corrections were not applied to either the transmission or the emission data but simulation studies indicated that scattering made only a small contribution to the attenuation measurement. Results are presented for two phantoms, in which transmission scans of 57,500 and 18,700 events/slice were used to correct emission images of 5.2 and 2.8 million events. Although the attenuation images had poor statistical accuracy and a resolution of 13 mm, the method resulted in accurate attenuation-corrected images with no degradation in image resolution (which was 3 mm for the first emission image), and with little effect on image noise.