Lucretiu M. Popescu

Iterative image reconstruction using geometrically ordered subsets with list-mode data

In positron emission tomography (PET), the format in which the data is stored has a major influence on the image reconstruction procedure. The use of the list-mode format preserves all of the measured attributes of the detected photon pairs but the events are stored in the order that they were measured, which allows only sequential access to the data. This fact limits the number of applicable algorithms and often computing speed or memory capacity constraints require the use of algorithms that do not make full use of the original precise information in the data. In this paper we show how through a change of the format in which the data is stored one can keep all the initial information about the individual events while providing random access to subsets of events belonging to given geometrical regions, thus making possible the use of maximum likelihood ordered subsets (OSEM) type algorithms with data provided as a collection of individual events (list-mode), and facilitating the adaptation of other types of algorithms. The structured data format also allows for more compact (compressed) storage of the information compared to the simple list-mode format.

Characterization of a time-of-flight PET scanner based on lanthanum bromide

A proto-type time-of-flight (TOF) 3D PET scanner based on lanthanum bromide detectors has been developed. The LaBr/sub 3/(5%Ce) Anger-logic detectors in this new scanner use 4/spl times/4/spl times/30 mm pixels and continuous light-guide coupled to a hexagonal array of 50-mm PMTs. The scanner consists of 24 modules with a 93-cm detector diameter and 25-cm axial field-of-view. Initial characterization of scanner performance has been performed, including energy and timing performance. We currently measure an overall system energy resolution of 7.5% and a system timing resolution is 460 ps, although we expect these results to improve eventually when the electronics are fully optimized. Since there are not yet standard tests to quantify the benefit of TOF, we designed two phantoms with hot and cold spheres in 27-cm and 35-cm diameter vessels to evaluate the TOF performance as a function of body size. The data from this scanner are reconstructed with a fully 3D list-mode iterative TOF algorithm with all data corrections incorporated into the system model. We find that TOF reconstruction reduces the noise and background variability, especially for the larger phantom representing a large patient. In addition, TOF improves detail and contrast of the spheres (lesions), especially the smallest 10-mm sphere. The TOF reconstruction reaches convergence faster than the non-TOF reconstruction, and the rate of convergence is seen to be more insensitive to object size. These results indicate that TOF will help improve image quality and potentially reduce scan time with clinical patients.

Nonparametric ROC and LROC analysis

In this paper we review several results of the nonparametric receiver operating characteristic (ROC) analysis and present an extension to the nonparametric localization ROC (LROC) analysis. Equations for the estimation of the area under the characteristic curve and for the variance calculations are derived. Expressions for the choice of the optimal ratio between the number of signal-absent and signal-present image samples are also presented. The results can be applied both with continuous or discrete scoring scales. The simulation studies carried out validate the theoretical derivations and show that the LROC analysis is considerably more sensitive than the ROC analysis.

Ray tracing through a grid of blobs

In this paper we describe two ray tracing algorithms for images represented using spherically symmetric basis functions (blobs) on regular grids. The method presented here allows more realistic modeling of the forward projection by considering tube shaped kernels, rather than simple lines. Each kernel is a function of the radial distance r from its center and can vary with the position l along the projection line. The forward projections are computed by convolutions of the kernel with the blob line integrals. Both ray tracing procedures presented incrementally compute the square distance r/sup 2/ for each visited blob enabling the appropriate resolution kernel to be used. The second variant also computes the l coordinate along the line of response axis allowing for longitudinal variations of the resolution kernel to be considered as well as time-of-flight (TOF) modeling.

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.

Investigation of image quality and NEC in a TOF-capable PET scanner

The purpose of this work is to determine the benefit which can be achieved in image quality for a time-of-flight (TOF) capable 3D whole-body PET scanner. We simulate a 3D whole-body time-of-flight PET scanner with a complete modeling of spatial and energy resolutions. The simulated scanner has a diameter of 84-cm, an axial FOV of 25-cm, and uses a 4times4times30-mm3 pixelated LaBr3 Anger-logic detector. Multiple simulations were performed for a 27-cm diameter and 70-cm long uniform cylinder with hot spheres (22,17,13, and 10-m diameter) in central slice, and 10-mm diameter hot spheres in a slice at 1/4 axial FOV (8:1 activity uptake ratio with respect to background). Image reconstruction was performed with a list-mode iterative TOF algorithm and data were currently analyzed for true coincidences after attenuation correction for timing resolutions of 300,600,1000-ps and non-TOF. Our results show that contrast recovery improves with TOF (NEMA NU2-2001 analysis). Detectability for 10-mm diameter hot spheres estimated using a non-prewhitening matched filter (NPW SNR) also improves with TOF and best results are obtained for timing resolution les300 ps

A versatile approach for Monte Carlo simulation of tomographic systems

In this paper we present the design principles and the main features of a new Monte Carlo simulation code for tomography that, through a modular object oriented approach, maintains the efficiency of specialized solutions while incorporating features common to general Monte Carlo particle transport simulation packages such as the presence of a comprehensive geometrical modeling subsystem. The simulation of photon history through a heterogeneous medium is treated as a distinct case of particle transport, rather than a geometrical representation problem, leading to efficient tracing through voxel-based anthropomorphic phantoms. The approach is general and flexible allowing for a mixed voxel and surface based representation of the attenuation distribution (similarly for the activity distribution). Various variance reduction techniques are introduced.

Comparison between TOF and non-TOF PET using a scan statistic numerical observer

Two dimensional time-of-flight (TOF) and non-TOF PET image sets are analyzed using a scan statistic (or maximum noise nodule search) observer, as well as a fixed position observer. The results reveal significant differences between the two approaches and indicate that the usual fixed position detectability evaluation techniques, often referred as signal known exactly background known exactly (SKE/BKE) evaluation tasks, insufficiently capture the true nature of image quality improvement that TOF information brings. We review here several results of the detection with localization theory and present a generalization using the noise nodule distribution in a given search area.

Dynamic Load Balancing on Distributed Listmode Time-of-Flight Image Reconstruction

A major obstacle in performing listmode reconstruction in PET imaging is the increased computation time compared to a conventional frame or histogrammed reconstruction. To overcome this challenge in a clinical setting, it is desirable to distribute the reconstruction task to multiple nodes. A previous work investigated the impact of high performance communication networks and focused mainly on static distribution. In practice, optimal static load balancing is difficult. Therefore we have developed a dynamic load balancing approach, which is flexible and can easily be adapted to a varying number of nodes, and the performance of which is not constrained by variation of the load levels of nodes needed for other tasks or by asymmetric network. In this approach, one of the nodes is designated as the distributor, whose task is to partition the events into small chunks and then distribute those chunks to other nodes for processing. Other nodes, which do the actual data processing, are called workers. Each worker requests a new chunk of data to process upon completion of an old one. In case of the OSEM algorithm, when all chunks have been processed in a subset, the workers are synchronized and the image is updated. This image forms the basis for the next subset. This system has been deployed in the Philips GEMINI-TF PET/CT system. For a whole-body patient scan of 150M events, the event processing time with 8 Xeon 3.6GHz dual-processor computers amounts to approximately 9 minutes for 3 iterations.

Maximum-likelihood estimation of scatter components algorithm for x-ray coherent scatter computed tomography of the breast

Coherent scatter computed tomography (CSCT) is a reconstructive x-ray imaging technique that yields the spatially resolved coherent-scatter cross section of the investigated object revealing structural information of tissue under investigation. In the original CSCT proposals the reconstruction of images from coherently scattered x-rays is done at each scattering angle separately using analytic reconstruction. In this work we develop a maximum likelihood estimation of scatter components algorithm (ML-ESCA) that iteratively reconstructs images using a few material component basis functions from coherent scatter projection data. The proposed algorithm combines the measured scatter data at different angles into one reconstruction equation with only a few component images. Also, it accounts for data acquisition statistics and physics, modeling effects such as polychromatic energy spectrum and detector response function. We test the algorithm with simulated projection data obtained with a pencil beam setup using a new version of MC-GPU code, a Graphical Processing Unit version of PENELOPE Monte Carlo particle transport simulation code, that incorporates an improved model of x-ray coherent scattering using experimentally measured molecular interference functions. The results obtained for breast imaging phantoms using adipose and glandular tissue cross sections show that the new algorithm can separate imaging data into basic adipose and water components at radiation doses comparable with Breast Computed Tomography. Simulation results also show the potential for imaging microcalcifications. Overall, the component images obtained with ML-ESCA algorithm have a less noisy appearance than the images obtained with the conventional filtered back projection algorithm for each individual scattering angle. An optimization study for x-ray energy range selection for breast CSCT is also presented.