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Component-based normalization is an important technique for PET scanners with a high number of lines of response (LOR), e.g., 4.5 x [10.sup.9] for the HRRT. It reduces the problem of measuring the sensitivity of each LOR to that of estimating the individual crystal efficiencies ([epsilon]), e.g., 119808 for the HRRT. We propose a component-based method to compute [epsilon] for the HRRT. In addition, the block design of the HRRT produces pulse pile-up which causes apparent changes in [epsilon] with count rate. These effects occur within the block and between the front (LSO) and back (LYSO) crystal layers. We use a rotating source to measure the [epsilon] values and a decaying uniform phantom to account for [epsilon] variations with count rate. The computation of efficiencies is achieved with ~1% statistical noise with an acquisition of ~1 h. Count rate dependency of [epsilon] is implemented as a linear model in terms of block singles rate. Four approaches to modify [epsilon] with count rate were compared. Among them, an independent parameter for each crystal produced the best results, both visually and quantitatively. Failure to account for the count rate dependency in [epsilon] leads to high resolution artifacts in the reconstructed images, most visible in the transverse plane, in the center of the field-of-view. Index Terms--Component-based normalization, HRRT, MOLAR, pile-up effect.

We investigated the influence of filter apodization and cutoff frequency on the image quality of volume positron emission tomography (PET) imaging using the three-dimensional reprojection (3-D RP) algorithm. An important parameter in 3-D RP and other filtered backprojection algorithms is the choice of the filter window function. In this study, the Hann, Hamming, and Butterworth low-pass window functions were investigated. For each window, a range of cutoff frequencies was considered. Projection data were acquired by scanning a uniform cylindrical phantom, a cylindrical phantom containing four small lesion phantoms having diameters of 3, 4, 5, and 6 mm and the 3-D Hoffman brain phantom. All measurements were performed using the high-resolution PET camera developed at the M.D. Anderson Cancer Center (MDAPET), University of Texas, Houston, TX. This prototype camera, which is a multiring scanner with no septa, has an intrinsic transaxial resolution of 2.8 mm. The evaluation was performed by computing the noise level in the reconstructed images of the uniform phantom and the contrast recovery of the 6-mm hot lesion in a warm background and also by visually inspecting images, especially those of the Hoffman brain phantom. For this work, we mainly studied the central slices which are less affected by the incompleteness of the 3-D data. Overall, the Butterworth window offered a better contrast-noise performance over the Hann and Hamming windows. For our high statistics data, for the Hann and Hamming apodization functions a cutoff frequency of 0.6-0.8 of the Nyquist frequency resulted in a reasonable compromise between the contrast recovery and noise level and for the Butterworth window a cutoff frequency of 0.4-0.6 of the Nyquist frequency was a reasonable choice. For the low statistics data, use of lower cutoff frequencies was more appropriate. Index Terms--Filtering, positron emission tomography (PET), three-dimensional (3-D) image reconstruction, 3-D reprojection (3-D RP).

A new detector design using pixelated NaI(T1) crystals has been evaluated for use in positron emission tomography (PET). This detector uses 4 x 4 x 30 [mm.sup.3] NAI(T1) pixels coupled via a lightguide (1.4 cm thick) to an array of 39 mm diameter photomultiplier tubes (PMTs) in an Anger detector design. Our measurements show that the high light output of NAI(T1) leads to a good discrimination of the 4 mm NAI(T1) pixels for varying integration times of 220,120, and 60 ns. The crystal-to-crystal variation in the measured energy for a central group of nine crystals is 1.1%, while the average energy resolution at 511 keV varies from 8.6% to 10.7% as the integration time decreases from 220 to 60 ns. Additionally, the measured light response function (LRF) of the pixelated detector is much narrower than that of the continuous, curveplate plate C-PET detectors, even though the pixelated crystal is thicker. High count-rate simulations for a whole-body scanner with pixelated NaI(T1) detectors but based on the C-PET geometry (diameter of 90 cm and an axial field-of-view of 25 cm) predict more than a doubling of the peak NEC rate over the C-PET scanner with curved, continuous detectors. This is due to the increased sensitivity of thicker crystals and reduced deadtime achieved by the pixelated detector design. Thus, a pixelated NAI(T1) detector based scanner offers significant improvements in both the spatial resolution and count-rate performance over the current whole-body C-PET scanner. Index Terms--Anger detector, discrete crystal, pixelated NaI(Tl) detector, positron emission tomography.

We describe two approaches to lossless compression of dynamic PET data. In the first, a sequence of sinogram frames are compressed using differential encoding followed by lossless entropy-based compression. The second approach applies lossless compression to data stored in a sinogram/timogram format in which the arrival times of each photon pair are stored in spatial order, indexed by the sinogram. Compression of the timogram is performed using entropic coding of the differential arrival times in each sinogram bin. We describe these compression methods and present results from simulated and real data comparing multiframe and sinogram/timogram formats. Both formats produce substantial reductions in data size compared to the raw data, with higher compression factors achieved using the sinogram/timogram format when high temporal resolution is required. Index Terms--Entropy, list-mode data, lossless compression.

We are developing an accelerated Monte Carlo simulation of positron emission tomography (PET) that can be used for scatter correction of three-dimensional (3-D) PET data. Our Monte Carlo technique accurately accounts for single, multiple, and dual Compton scatter events, attenuation through the patient bed, and activity from outside the field of view. We have incorporated innovative sampling techniques that are compatible with our simulation approach, increasing computational efficiency by a factor of seven while improving accuracy through more sophisticated stratification and by incorporating the true energy response of the scanner. The required execution time to acquire 10 million scatter coincidence events for a 3-D thorax PET scan is only 4 min on a 300-MHz Sun dual-processor workstation. We demonstrate that for a low-noise thorax phantom study, image data corrected using the Monte Carlo 3-D PET scatter correction demonstrate no statistically significant deviation from the true activity concentration provided corresponding input data are accurate. The speed and accuracy of our simulation makes it an efficient research tool for studying scatter effects in PET and a practical scatter correction for 3-D PET clinical imaging. Index Terms--Compton scatter, Monte Carlo simulation, photon tracking, positron emission tomography (PET), sampling techniques, scatter correction, three-dimensional (3-D) PET, variance reduction.

Tomographic image reconstruction using statistical methods can provide more accurate system modeling, statistical models, and physical constraints than the conventional filtered backprojection (FBP) method. Because of the ill posedness of the reconstruction problem, a roughness penalty is often imposed on the solution to control noise. To avoid smoothing of edges, which are important image attributes, various edge-preserving regularization methods have been proposed. Most of these schemes rely on information from local neighborhoods to determine the presence of edges. In this paper, we propose a cost function that incorporates nonlocal boundary information into the regularization method. We use an alternating minimization algorithm with deterministic annealing to minimize the proposed cost function, jointly estimating region boundaries and object pixel values. We apply variational techniques implemented using level-sets methods to update the boundary estimates; then, using the most recent boundary estimate, we minimize a space-variant quadratic cost function to update the image estimate. For the positron emission tomography transmission reconstruction application, we compare the bias-variance tradeoff of this method with that of a 'conventional' penalized-likelihood algorithm with local Huber roughness penalty. Index Terms--Edge-preserving reconstruction, level sets, positron emission tomography (PET), region-based, transmission tomography.

We consider a class of estimation problems in which data of a Poisson character are related by a linear model to a target function that satisfies certain physical constraints. The [...]

In previous works, the determination of object and detector scatter kernels from line source measurements was described and their application in scatter correction was investigated. It was also shown that low energy data contains a large fraction of useful events (true and detector scatter events). In the present work, data acquired in multispectral mode was summed in single broad energy windows of lower energy thresholds varying from 129 to 516 keV in steps of 43 keV and a constant upper energy threshold of 645 keV. Line-source projections were fitted by extracting the object and detector scatter kernels as a function of energy threshold. These kernels were then used to process scatter by the nonstationary convolution subtraction-restoration method in phantom images. After scatter correction, the sensitivity is found to increase by up to 64% at the lower threshold of 129 keV, relative to the conventional photopeak energy window (344-645 keV). Whereas contrast and spatial resolution are degraded as the energy discriminator is lowered, such degradation is fully recovered by the scatter correction. As a result of scatter correction, the noise increases insignificantly in hot regions but substantially in cold regions, in proportion of the amount of scatter. Index Terms - Nonstationary, positron emission tomography, scatter correction, scatter subtraction-restoration.

Various models have been proposed to quantitate from [18F]-Fluoro-Deoxy-Glucose ([18F]FDG) positron emission tomography (PET) data glucose regional metabolic rate. We evaluate here four models, a three-rate constants (3K) model, a four-rate constants (4K) model, an heterogeneous model (TH) and a spectral analysis (SA) model. The data base consists of [18F]FDG dynamic data obtained in the myocardium and brain gray and white matter. All models were identified by nonlinear weighted least squares with weights chosen optimally. We show that: 1) 3K and 4K models are indistinguishable in terms of parsimony criteria and choice should be made on parameter precision and physiological plausibility: in the gray matter a more complex model than the 3K one is resolvable; 2) the TH model is resolvable in the gray but not in the white matter: 3) the classic SA approach has some unnecessary hypotheses built in and can be in principle misleading: we propose here a new SA model which is more theoretically sound; 4) this new SA approach supports the use of a 3K model in the heart with a 60 rain experimental period: it also indicates that heterogeneity in the brain is modest in the white matter; 5) [18F]FDG fractional uptake estimates of the four models are very close in the heart, but not in the brain; 6) a higher than 60 min experimental time is preferable for brain studies. Index Terms - Fluoro-deoxy-glucose (FDG), glucose, kinetics metabolism, model identification, parameter estimation, physiological model, tracer.

Accurate quantitation of small lesions with positron emission tomography (PET) requires correction for the partial volume effect. Traditional methods that use Gaussian models of the PET system were found to be insufficient. A new approach that models the non-Gaussian object-dependent scatter was developed. The model consists of eight simple functions with a total of 24 parameters. Images of line and disk sources in circular and elliptical cylinders, and an anthropomorphic chest phantom were used to determine the parameter values. Empirical rules to determine these parameter values for various objects based on those for a reference object, a 21.5-cm circular cylinder, were also proposed. For seven spheroids and a 3.4-cm cylinder, pixel values predicted by the model were compared with the measured values. The model-to-measurement-ratio was 1.03 [+ or -] 0.07 near the center of the spheroids and 0.99 [+ or -] 0.03 near the center of the 3.4-cm cylinder. In comparison, the standard single Gaussian model had corresponding ratios of 1.27 [+ or -] 0.09 and 1.24 [+ or -] 0.03, respectively, and the corresponding ratios for a double Gaussian model were 1.13 [+ or -] 0.09 and 1.05 [+ or -] 0.01. Scatter fraction (28.5%) for a line source in the 21.5-cm cylinder was correctly estimated by our model. Because of scatter, we found that errors in the measurement of activity in spheroids with diameters from 0.6 to 3.4 cm were more significant than previously appreciated. Index Terms - Point spread function, scatter, partial volume effect, positron emission tomography.

Objective evaluation of dynamic imaging protocols needs a realistic simulation tool to model the data acquisition and image reconstruction of a PET system. Availability of the correlated functional and anatomical images in many centers allows the creation of highly realistic objects to represent brain activity and attenuation distribution for each study. We have developed a fast analytical model that incorporates key physical factors inherent in coincidence detection along with spatially variant 3-D detection efficiency and deadtime. In this paper we use MR and PET data of a 3-D Hoffman brain phantom to demonstrate and validate our computational methods. The simulated total projection, attenuation factor, and scatter profiles are in very good agreement with the experimental data. The corresponding regional activity values in the gray matter and white matter have a discrepancy of [less than or equal to] 8.5 %. We also show typical emission and transmission images generated from MR brain scans. This tool is particularly useful in evaluating projection data processing and image reconstruction algorithms.

We present a count rate model for PET. Considering a standard 20x20 cm phantom in the field-of-view of a cylindrical septaless tomograph, the model computes the acceptance to prompt and random events from simple geometric considerations. Dead time factors at all stages of a typical event acquisition architecture are calculated from specified processing clock cycles. Validations of the model's predictions against the measured performances of the ECAT-953B and the EXACT HR PLUS are presented. The model is then used to investigate the benefit of using detectors made of LSO in the EXACT HR PLUS scanner geometry. The results indicate that in replacing BGO by the faster LSO, one can count on an increase of the peak noise-equivalent-count rate by a factor 2.2. This gain will be achieved by using a 5 nsec coincidence window, buckets operating on a 128 nsec clock cycle, and a front-end data acquisition that can sustain a total event rate of 2.9 MHz.

Whole-body positron emission tomography (PET) has recently emerged as an important imaging tool for cancer detection and staging. Initial applications of the technique have been primarily qualitative. One of the major reasons is the limits imposed by kinetically undersampled data over the whole body, as opposed to the standard method of continuous dynamic sampling in one body location. In this paper, a new estimation method using weighted nonlinear least squares (WNLS) for the first bed position and Bayesian regression (BR) for subsequent positions is proposed. A general criterion for designing optimal sampling schedules which maximizes the measurement information with multiple bed positions is developed. The overall approach is illustrated with the problem of estimating the metabolic rate of glucose (MRGlu) in tumors at different axial positions (image bed positions) in the body by using computer simulations and patient data. The results show that estimates of MRGlu using sparse data and the optimized Bayesian approach are comparable with those obtained by standard methods and fully sampled data. This study demonstrates the potential of the technique described for quantification where several bed positions have to be used to image all the regions of interest (ROI).

A new double modeling approach for dynamic cardiac studies with positron emission tomography (PET) to estimate physiological parameters is proposed. This approach is exemplified by tracer fluorodeoxyglucose (FDG) studies and estimation of myocardial metabolic rate of glucose (MMRGlc). A separate input function model characterising the tracer kinetics in plasma is used to account for the measurement noise and spillover problems of the input curve obtained from the left ventricular region on the PET images. Measured left ventricle (LV) plasma time-activity and tissue time-activity curves are fitted simultaneously with cross contaminations by this input function model and the FDG model. The results indicate that the MMRGlc can be estimated much more accurately and reliably by this new approach. Compared with the traditional method, an improvement of about 20% in the estimated MMRGlc was achieved when the bidirectional spillover fractions are 20% at different noise levels studied. This new double modeling approach using two models fitting both the input and the output functions simultaneously is expected to be generally applicable to a broad range of system modeling.

The image space reconstruction algorithm (ISRA) was proposed as a modification of the expectation maximization (EM) algorithm based on physical considerations for application in volume emission computed tomography. As a consequence of this modification, ISRA searches for least squares solutions instead of maximizing Poisson likelihoods as the EM algorithm. In this paper, we show that both algorithms may be obtained from a common mathematical framework. We use this fact to extend ISRA for penalized likelihood estimates.

The work presented in this paper evaluates the statistical characteristics of regional bias and expected error in reconstructions of real PET data of human brain fluorodeoxiglucose (FDG) studies carried out by the maximum likelihood estimator (MLE) method with a robust stopping rule, and compares them with the results of filtered backprojection (FBP) reconstructions and with the method of sieves. The task that we have investigated is that of quantifying radioisotope uptake in regions-of-interest (ROI's). We first describe a robust methodology for the use of the MLE method with clinical data which contains only one adjustable parameter: the kernel size for a Gaussian filtering operation that determines final resolution and expected regional error. Simulation results are used to establish the fundamental characteristics of the reconstructions obtained by our methodology, corresponding to the case in which the transition matrix is perfectly known. Then, data from 72 independent human brain FDG scans from four patients are used to show that the results obtained from real data are consistent with the simulation, although the quality of the data and of the transition matrix have an effect on the final outcome. The most important results are that, for equal resolution, expected pixel-by-pixel error in the MLE and sieves reconstructions are lower in the regions of low counts than in the regions of high counts, the lowest being for the MLE. In contrast, FBP reconstructions show an expected error that is high and nearly independent of the number of counts in a region. As a consequence, the determination of radioisotope uptake in ROI's of high activity has approximately the same standard deviation in MLE, sieves, and FBP reconstructions, while the standard deviation in ROI's of low uptake is substantially lower for MLE, while sieves take an intermediate value. The use of a well-constructed Monte Carlo transition matrix improves all the results with real data in a measurable way. We conclude that our proposed MLE methodology and the method of sieves have a definite advantage over FBP. There is a tradeoff between shorter computation time, a slight bias but lower standard deviation for MLE and longer computation time, a basically unbiased estimation but higher standard deviation for sieves.

An approximation formula for the variance of Positron Emission Tomography (PET) region-of-interest (ROI) values has been developed, implemented, and evaluated. This formula does not require access to the original projection data and is therefore convenient for routine use. The formula was derived by applying successive approximations to the filtered-backprojection reconstruction algorithm. ROI variance is estimated from the product of mean pixel variance within the region and a term accounting for the intercorrelation of all pixel pairs inside the region. The formula accounts for radioactivity distribution, attenuation, randoms, scatter, deadtime, detector normalization, scan length, decay, and reconstruction filter. The algorithm was tested by comparison to the exact ROI variance as calculated with Huesman's algorithm. Tests with scan data from phantoms, animals, and humans obtained on the Scanditronix PC2048-15B tomograph showed the approximation formula to be accurate to within |+ or -~10 percent.

The EM algorithm is the basic approach used to maximize the log likelihood objective function for the reconstruction problem in PET. The EM algorithm is a scaled steepest ascent algorithm that elegantly handles the nonnegativity constraints of the problem. We show that the same scaled steepest descent algorithm can be applied to the least squares merit function, and that it can be accelerated using the conjugate gradient approach. Our experiments suggest that one can cut the computation by about a factor of 3 by using this technique. Our results also apply to various penalized least squares functions which might be used to produce a smoother image.

A simple spatial-correlation model is presented for repeated measures data. Correlation between observations on the same subject is assumed to decay as a linear function of the squared distance separating the regions in three-dimensional space where the observations are made. This quadratic decay (QD) model has many attractive theoretical properties. The covariance structure of the 'normalized' data, formed by subtracting the subject average, is the same as that generated by random linear trends plus centered white noise, which leads to a simple method for simulating the original data. It also implies that the first three principal components of the normalized observations are the spatial coordinates of the regions. Thus principal components analysis can be used as an exploratory tool to verify the QD model, provided the white noise component is small. Certain simple predictions can be made, such as the fact that the variances of the normalized observations increase linearly with the squared distance from the centroid of the regions, even though the original observations are assumed to have equal variance. This implies that it is harder to detect abnormal regional measurements in the outlying regions using normalized observations. Assuming multivariate normality, generalized least squares can be used to find maximum likelihood estimates of the QD model; calculations can be reduced using an expression for the inverse of the covariance matrix that only involves the inverse of a 3 x 3 matrix. It is shown, however, that although normalization simplifies the model by removing the random subject effect, it reduces information about the spatial correlation effect, making it harder to detect. This may have implications for other spatial-correlation models that are fitted to residuals from a sample mean. The QD model is applied to 30 cerebral regional glucose metabolism measurements from positron emission tomography (PET) images on a group of 20 normal subjects. KEY WORDS: Covariance structures; Generalized least squares; Permutation tests; Repeated measures., 1. THE DATA A set of n anatomical regions of the brain, indexed by i = 1, ..., n, can be identified on positron emission tomography (PET) images, and in [...]

The combination of Fourier rebinning (FORE) and the ordered subsets expectation-maximization (OSEM), a fast statistical algorithm, appears as a promising alternative to the fully three-dimensional (3-D) iterative approach for clinical positron emission tomography (PET) data. In this paper, we evaluated the properties of FORE+OSEM and compared it with fully 3-D OSEM using both simulations and data acquired by commercial scanners. The aim is to determine to what extent the speed advantage of FORE+OSEM is paid for by a possible degradation of image quality in the case of noisy clinical PET data. A forward- and back-projection pair based on a line integral model was used in two-dimensional OSEM and 3-D OSEM (3D-OSEM) instead of a system matrix. Different variants of both approaches have been studied with simulations in terms of contrast-noise tradeoff. Two variants -- FORE+OSEM with attenuation weighting (AW) [FORE+OSEM(AW)] and 3D-OSEM with attenuation-normalization weighting (ANSP) and a shifted-Poisson (SP) model [3D-OSEM(ANSP)]--were compared with measured phantom data and patient data. Based on the results from both simulations and measured data, we conclude that: 1) both attenuation (-normalization) weighting and the SP model improve the image quality but slow down the convergence and 2) despite its approximate nature, FORE+OSEM does not show apparent image degradation compared with 3D-OSEM for data with a noise level typical of a whole-body FDG scan. Index Terms--PET, rebinning, statistical reconstruction.

We describe the electronics for a high-performance positron emission mammography (PEM) camera. It is based on the electronics for a human brain positron emission tomography (PET) camera (the Siemens/CTI HRRT), modified to use a detector module that incorporates a photodiode (PD) array. An application-specified integrated circuit (ASIC) services the photodetector (PD) array, amplifying its signal and identifying the crystal of interaction. Another ASIC services the photomultiplier tube (PMT), measuring its output and providing a timing signal. Field-programmable gate arrays (FPGAs) and lookup RAMs are used to apply crystal-by-crystal correction factors and measure the energy deposit and the interaction depth (based on the PD/PMT ratio). Additional FPGAs provide event multiplexing, derandomization, coincidence detection, and real-time rebinning. Embedded PC/104 microprocessors provide communication, real-time control, and configure the system. Extensive use of FPGAs make the overall design extremely flexible, allowing many different functions (or design modifications) to be realized without hardware changes. Incorporation of extensive onboard diagnostics, implemented in the FPGAs, is required by the very high level of integration and density achieved by this system.

A set of preliminary test results of a detector prototype for positron emission tomography applications is presented. The detector is made of a YAP:Ce finger crystal (2 x 2 x 30 [mm.sup.3] each) matrix coupled to a set of square section wavelength-shifting fibers (one fiber for each matrix row and one fiber for each matrix column) read by a position-sensitive detector. The recognition of each fiber allows the determination of the x-y position of the scintillation event. The light yield of the system has been investigated: all possible light loss factors have been taken into account to evaluate the expected signal. Experimental measurements with a single-pixel hybrid photodiodes have been performed. We have measured about ten photoelectrons for a deposit of 511 keV in the scintillator for each coordinate. Preliminary position measurements with a small 5 x 5 matrix are presented.

Novel conjugate-gradient preconditioners are proposed for shift-variant positron emission tomography (PET) image reconstruction. The preconditioners approximate more accurately the Hessian matrices of shift-variant imaging problems and produce faster convergence rates for the unconstrained conjugate-gradient iteration than diagonal or circulant preconditioners. An efficient procedure for the line-search step required by conjugate-gradient methods is also presented.