Modelling and Simulation of Compton Scatter Image Formation in Positron Emission Tomography.

We present the comparative study of the analytical forward model and the statistical simulation of the Compton single scatter in the Positron Emission Tomography. The formula of the forward model has been obtained using the Single Scatter Simulation approximation under simplified assumptions and therefore we calculate scatter projections using independent Monte Carlo simulation mimicking the scatter physics. The numerical comparative study has been performed using a digital cylindrical phantom filled in with water and containing spherical sources of emission activity located at the central and several displaced positions. Good fits of the formula-based and statistically generated profiles of scatter projections are observed in the presented numerical results.

Efficient 3-D TOF PET reconstruction using view-grouped histo-images: DIRECT-direct image reconstruction for TOF.

For modern time-of-flight (TOF) positron emission tomography (PET) systems, in which the number of possible lines of response and TOF bins is much larger than the number of acquired events, the most appropriate reconstruction approaches are considered to be list-mode methods. However, their shortcomings are relatively high computational costs for reconstruction and for sensitivity matrix calculation. Efficient treatment of TOF data within the proposed DIRECT approach is obtained by 1) angular (azimuthal and co-polar) grouping of TOF events to a set of views as given by the angular sampling requirements for the TOF resolution, and 2) deposition (weighted-histogramming) of these grouped events, and correction data, into a set of "histo-images," one histo-image per view. The histo-images have the same geometry (voxel grid, size and orientation) as the reconstructed image. The concept is similar to the approach involving binning of the TOF data into angularly subsampled histo-projections-projections expanded in the TOF directions. However, unlike binning into histo-projections, the deposition of TOF events directly into the image voxels eliminates the need for tracing and/or interpolation operations during the reconstruction. Together with the performance of reconstruction operations directly in image space, this leads to a very efficient implementation of TOF reconstruction algorithms. Furthermore, the resolution properties are not compromised either, since events are placed into the image elements of the desired size from the beginning. Concepts and efficiency of the proposed data partitioning scheme are demonstrated in this work by using the DIRECT approach in conjunction with the row-action maximum-likelihood (RAMLA) algorithm.

Small nodule detectability evaluation using a generalized scan-statistic model.

In this paper is investigated the use of the scan statistic for evaluating the detectability of small nodules in medical images. The scan-statistic method is often used in applications in which random fields must be searched for abnormal local features. Several results of the detection with localization theory are reviewed and a generalization is presented using the noise nodule distribution obtained by scanning arbitrary areas. One benefit of the noise nodule model is that it enables determination of the scan-statistic distribution by using only a few image samples in a way suitable both for simulation and experimental setups. Also, based on the noise nodule model, the case of multiple targets per image is addressed and an image abnormality test using the likelihood ratio and an alternative test using multiple decision thresholds are derived. The results obtained reveal that in the case of low contrast nodules or multiple nodules the usual test strategy based on a single decision threshold underperforms compared with the alternative tests. That is a consequence of the fact that not only the contrast or the size, but also the number of suspicious nodules is a clue indicating the image abnormality. In the case of the likelihood ratio test, the multiple clues are unified in a single decision variable. Other tests that process multiple clues differently do not necessarily produce a unique ROC curve, as shown in examples using a test involving two decision thresholds. We present examples with two-dimensional time-of-flight (TOF) and non-TOF PET image sets analysed using the scan statistic for different search areas, as well as the fixed position observer.

PET energy-based scatter estimation and image reconstruction with energy-dependent corrections.

In this paper we propose a comprehensive energy-based scatter correction approach for positron emission tomography (PET). We take advantage of the marked difference between the energy spectra of the unscattered and scattered photons, and use the detailed energy information that comes with the list-mode data for the estimation of the scattered events distribution in the data space. Also, inside the maximum-likelihood expectation maximization (ML-EM) image reconstruction algorithm, we introduce energy-dependent factors that individualize the correction terms for each event, given its position and energy information. The central piece of our approach is the two-dimensional detector energy response model represented as a linear combination of four components, each one representing a particular state a PET event can be found in: both photons unscattered, the second scattered while the first not, the first photon scattered while the second not and both photons scattered. For a set of events collected in the vicinity of a point in the projection space, the coefficient of each component is determined by applying a statistical estimator. As a result we obtain the number of scattered events that are in the given set. The model also gives us the variation of scatter fraction with the photon pair energies for that particular position in the data space. A simulation study that demonstrates the proposed methods is presented.

Fast reconstruction of 3D time-of-flight PET data by axial rebinning and transverse mashing.

Faster scintillators like LaBr(3) and LSO have sparked renewed interest in PET scanners with time-of-flight (TOF) information. The TOF information adds another dimension to the data set compared to conventional three-dimensional (3D) PET with the size of the projection data being multiplied by the number of TOF bins. Here we show by simulations and analytical reconstruction that angular sampling for two-dimensional (2D) TOF PET can be reduced significantly compared to what is required for conventional 2D PET. Fully 3D TOF PET data, however, have a wide range of oblique and transverse angles. To make use of the smaller necessary angular sampling we reduce the 3D data to a set of 2D histoprojections. This is done by rebinning the 3D data to 2D data and by mashing these 2D data into a limited number of angles. Both methods are based on the most likely point given by the TOF measurement. It is shown that the axial resolution loss associated with rebinning reduces with improved timing resolution and becomes less than 1 mm for a TOF resolution below 300 ps. The amount of angular mashing that can be applied without tangential resolution loss increases with improved TOF resolution. Even quite coarse angular mashing (18 angles out of 324 measured angles for 424 ps) does not significantly reduce image quality in terms of the contrast or noise. The advantages of the proposed methods are threefold. Data storage is reduced to a limited number of 2D histoprojections with TOF information. Compared to listmode format we have the advantage of a predetermined storage space and faster reconstruction. The method does not require the normalization of projections prior to rebinning and can be applied directly to measured listmode data.