Using an external gating signal to estimate noise in PET with an emphasis on tracer avid tumors

Abstract

The purpose of this study is to establish and validate a methodology for estimating the standard deviation of voxels with large activity concentrations within a PET image using replicate imaging that is immediately available for use in the clinic. To do this, ensembles of voxels in the averaged replicate images were compared to the corresponding ensembles in images derived from summed sinograms. In addition, the replicate imaging noise estimate was compared to a noise estimate based on an ensemble of voxels within a region. To make this comparison two phantoms were used. The first phantom was a seven-chamber phantom constructed of 1 liter plastic bottles. Each chamber of this phantom was filled with a different activity concentration relative to the lowest activity concentration with ratios of 1:1, 1:1, 2:1, 2:1, 4:1, 8:1 and 16:1. The second phantom was a GE Well-Counter phantom. These phantoms were imaged and reconstructed on a GE DSTE PET/CT scanner with 2D and 3D reprojection filtered backprojection (FBP), and with 2D- and 3D-ordered subset expectation maximization (OSEM). A series of tests were applied to the resulting images that showed that the region and replicate imaging methods for estimating standard deviation were equivalent for backprojection reconstructions. Furthermore, the noise properties of the FBP algorithms allowed scaling the replicate estimates of the standard deviation by a factor of 1/square root N, where N is the number of replicate images, to obtain the standard deviation of the full data image. This was not the case for OSEM image reconstruction. Due to nonlinearity of the OSEM algorithm, the noise is shown to be both position and activity concentration dependent in such a way that no simple scaling factor can be used to extrapolate noise as a function of counts. The use of the Well-Counter phantom contributed to the development of a heuristic extrapolation of the noise as a function of radius in FBP. In addition, the signal-to-noise ratio for high uptake objects was confirmed to be higher with backprojection image reconstruction methods. These techniques were applied to several patient data sets acquired in either 2D or 3D mode, with (18)F (FLT and FDG). Images of the standard deviation and signal-to-noise ratios were constructed and the standard deviations of the tumors' uptake were determined. Finally, a radial noise extrapolation relationship deduced in this paper was applied to patient data.

Rationale, Instrumental Accuracy, and Challenges of PET Quantification for Tumor Segmentation in Radiation Treatment Planning

“…While all modern PET scanners are supplied with and clinics use statistically based (iterative) image reconstruction, it is useful to discuss the resolution and noise properties of images generated with older, deterministic, image reconstruction methods first. In deterministic image reconstruction methods, such as filtered back-projection, the back-projection process mixes the Poisson distributed projection data via the projection operator (often a uniformly spaced Radon transform) to generate images whose voxels have a Gaussian noise distribution (Alpert et al, 1982;Schmidtlein et al, 2010). The resulting images have better signal-to-noise ratios for high contrast objects than for low contrast objects (this is not true for OSEM, as explained below).…”

“…However, like all un-regularized maximum likelihood estimates, these reconstruction methods begin to fit the noise of the data if iterated too many times. Furthermore, the signal-to-noise (SNR) ratio over the image is more uniform, and because of that hot objects will have higher noise compared to colder objects (Schmidtlein et al, 2010). As a result, the ability of iterative statistical reconstruction to produce increased contrast in low uptake regions is one of the primary reasons that these methods are superior to deterministic methods for diagnostic purposes.…”

“…It follows then from the proportionality and the nonuniform sampling that the noise and resolution properties in these images are position dependent (Fessler & Rogers, 1996). In addition, the covariance between neighboring voxels is increased, that adds complexity when evaluating the statistical properties of regions of interest (Buvat 2002;Schmidtlein et al, 2010). Following iterative reconstruction, most data is typically smoothed to reduce the effects of the data over-fitting.…”

“…Noting this and using the approximation that, for MLEM reconstructed images, the variances of the data are proportional to the square of the mean , ≅ , (Barrett et al, 1994;Schmidtlein et al, 2010), and evaluating at this can be rewritten to give the effect of noise on segmentation as,…”

“…The above formalism ignores the covariance between neighboring voxels. In practice, the covariance can be included and estimated as shown by Buvat (Buvat, 2002), and the variance can be estimated by using a staggered checkerboard pattern (Schmidtlein et al, 2010). Although slowly varying photon scatter can affect local intensities due to the effect of attenuation correction (Fig.10); the effects of severe over-correction can confound segmentation Random Coincidences Generally negligible effects due to accurate corrections Depth of Interaction Decreased spatial resolution and increased edge uncertainty Electronics Dead Time Can affect voxel intensities and also the scatter fraction estimate Image Reconstruction Parameters of iterative reconstruction (e.g., iteration number, post-reconstruction filters) modify the smoothness of an image to which segmentation methods are sensitive Registration with the Attenuation Image Attenuation artifacts and scatter artifacts…”