Evren Asma

Spatiotemporal reconstruction of list-mode PET data

We describe a method for computing a continuous time estimate of tracer density using list-mode positron emission tomography data. The rate function in each voxel is modeled as an inhomogeneous Poisson process whose rate function can be represented using a cubic B-spline basis. The rate functions are estimated by maximizing the likelihood of the arrival times of detected photon pairs over the control vertices of the spline, modified by quadratic spatial and temporal smoothness penalties and a penalty term to enforce nonnegativity. Randoms rate functions are estimated by assuming independence between the spatial and temporal randoms distributions. Similarly, scatter rate functions are estimated by assuming spatiotemporal independence and that the temporal distribution of the scatter is proportional to the temporal distribution of the trues. A quantitative evaluation was performed using simulated data and the method is also demonstrated in a human study using /sup 11/C-raclopride.

PET image reconstruction using anatomical information through mutual information based priors

We propose a non-parametric method for incorporating information from co-registered anatomical images into PET image reconstruction through priors based on mutual information. Mutual information between feature vectors extracted from the anatomical and functional images is used as a priori information in a Bayesian framework for the reconstruction of the PET image. The computation of mutual information requires an estimate of the joint density of the two images, which is obtained by using the Parzen window method. Preconditioned conjugate gradient with a bent Armijo line-search is used to maximize the resulting posterior density. The performance of this method is compared with that using a Gaussian quadratic penalty, which does not use anatomical information. Simulation results are presented for PET and MR images generated from a slice of the Hoffman brain phantom. These indicate that mutual information based penalties can potentially provide superior quantitation compared to Gaussian quadratic penalties

Model-based normalization for iterative 3D PET image reconstruction.

We describe a method for normalization in 3D PET for use with maximum a posteriori (MAP) or other iterative model-based image reconstruction methods. This approach is an extension of previous factored normalization methods in which we include separate factors for detector sensitivity, geometric response, block effects and deadtime. Since our MAP reconstruction approach already models some of the geometric factors in the forward projection, the normalization factors must be modified to account only for effects not already included in the model. We describe a maximum likelihood approach to joint estimation of the count-rate independent normalization factors, which we apply to data from a uniform cylindrical source. We then compute block-wise and block-profile deadtime correction factors using singles and coincidence data, respectively, from a multiframe cylindrical source. We have applied this method for reconstruction of data from the Concorde microPET P4 scanner. Quantitative evaluation of this method using well-counter measurements of activity in a multicompartment phantom compares favourably with normalization based directly on cylindrical source measurements.

Accurate estimation of the fisher information matrix for the PET image reconstruction problem

The Fisher information matrix (FIM) plays a key role in the analysis and applications of statistical image reconstruction methods based on Poisson data models. The elements of the FIM are a function of the reciprocal of the mean values of sinogram elements. Conventional plug-in FIM estimation methods do not work well at low counts, where the FIM estimate is highly sensitive to the reciprocal mean estimates at individual detector pairs. A generalized error look-up table (GELT) method is developed to estimate the reciprocal of the mean of the sinogram data. This approach is also extended to randoms precorrected data. Based on these techniques, an accurate FIM estimate is obtained for both Poisson and randoms precorrected data. As an application, the new GELT method is used to improve resolution uniformity and achieve near-uniform image resolution in low count situations.

Internet2-based 3D PET image reconstruction using a PC cluster

We describe an approach to fast iterative reconstruction from fully three-dimensional (3D) PET data using a network of PentiumIII PCs configured as a Beowulf cluster. To facilitate the use of this system, we have developed a browser-based interface using Java. The system compresses PET data on the users machine, sends these data over a network, and instructs the PC cluster to reconstruct the image. The cluster implements a parallelized version of our preconditioned conjugate gradient method for fully 3D MAP image reconstruction. We report on the speed-up factors using the Beowulf approach and the impacts of communication latencies in the local cluster network and the network connection between the users machine and our PC cluster.

Mean and covariance properties of dynamic PET reconstructions from list-mode data

We derive computationally efficient methods for the estimation of the mean and variance properties of penalized likelihood dynamic positron emission tomography (PET) images. This allows us to predict the accuracy of reconstructed activity estimates and to compare reconstruction algorithms theoretically. We combine a bin-mode approach in which data is modeled as a collection of independent Poisson random variables at each spatiotemporal bin with the space-time separabilities in the imaging equation and penalties to derive rapidly computable analytic mean and variance approximations. We use these approximations to compare bias/variance properties of our dynamic PET image reconstruction algorithm with those of multiframe static PET reconstructions.

4D PET image reconstruction from list mode data

We describe a method for computing a continuous time estimate of tracer density using list mode PET data. The rate function in each voxel is modeled as an inhomogeneous Poisson process whose rate function can be represented using a cubic B-spline basis. The rate functions are estimated by maximizing the likelihood of the arrival times of detected photon pairs over the control vertices of the spline, modified by quadratic spatial and temporal smoothness penalties and a penalty term to enforce non-negativity. Random rate functions are estimated by assuming independence between the spatial and temporal randoms distributions. Similarly, scatter rate functions are estimated by assuming spatiotemporal independence and that the temporal distribution of the scatter is proportional to the temporal distribution of the trues. A quantitative evaluation was performed using simulated data and the method was also demonstrated in human studies using O-15 water and C-11 raclopride.

Accurate and consistent lesion quantitation with clinically acceptable penalized likelihood images

Clinical widespread use of edge-preserving penalized-likelihood (PL) methods has been hindered by the properties of the resulting images such as blocky background noise textures, piecewise-constant appearances of organs and relative noise strengths in high and low activity regions despite their potential for improved lesion quantitation over OSEM and quadratically penalized PL. Here, we investigate the use of the convex relative difference penalty first introduced by Nuyts et at. (TNS 02) for improved quantitation over OSEM in whole-body clinical PET imaging while maintaining visual image properties similar to OSEM and therefore clinical acceptability. We perform data-independent axial smoothing modulation based on the system sensitivity profile in order to avoid excessively smooth bed-position overlap regions. We also perform data-independent transaxial smoothing modulation to avoid oversmoothing the central portions of the field-of-view that occur with the use of a constant smoothing parameter. The resulting overall smoothing modulation profile allows for improved resolution uniformity in regions with high sensitivity and improved noise uniformity between regions of low and high sensitivity. We evaluate our approach in multiple clinical datasets with lesions inserted into representative locations with time-of-flight (TOF) and non-TOF reconstructions. Such hybrid datasets combine clinically realistic image backgrounds with known lesion activities. We demonstrate that using the relative difference penalty with proper smoothing modulation, superior quantitation over early-stopped and post-filtered OS EM can be achieved while maintaining clinically acceptable image quality. Furthermore, the approach lends itself to theoretical contrast recovery prediction and bias correction for improved contrast recovery consistency across lesions and further improvements in quantitation.

A fast fully 4D incremental gradient reconstruction algorithm for list mode PET data

We present a fully four-dimensional, globally convergent, incremental gradient algorithm to estimate the continuous-time tracer density from list mode positron emission tomography (PET) data. The rate function in each voxel is modeled as an inhomogeneous Poisson process whose rate function can be reconstructed using a cubic B-spline basis. The rate functions are then estimated by maximizing the objective function formed by the sum of the likelihood of arrival times and spatial and temporal smoothness penalties. We first provide a computable bound for the norms of the optimal temporal basis function coefficients, and based on this bound we construct an incremental gradient algorithm that converges to the solution. Fully four-dimensional simulations demonstrate the convergence of the algorithm for a high count dataset on a 4-ring scanner.

Analysis of organ uniformity in low count density penalized likelihood PET images

We evaluated the organ uniformity properties of post-smoothed OSEM and penalized-likelihood (PL) images reconstructed with quadratic and non-quadratic penalties from low count PET datasets. Tumor contrast, background noise strength and background noise correlation length properties were jointly used to compare bias, variance and covariance tradeoffs within uniform organs in PL and post-smoothed OSEM images. Contrast was measured as the ratio of mean tumor and mean background activities. Noise variance was measured as the average ensemble standard deviation of the background voxels. Noise correlation lengths were measured indirectly via a non-uniformity metric as the standard deviation of the means inside 15 background spheres. Short noise correlation lengths gave small non-uniformity values while those comparable to sphere dimensions resulted in larger values. Simulated 2D and 3D datasets with less than 3 counts per sinogram bin were reconstructed using post-smoothed OSEM and PL with quadratic, logcosh, Huber and generalized Gaussian penalties. The generalized Gaussian penalty with proper parameter selection, was able to provide images with both higher contrast and shorter noise correlation lengths at matched noise strength. Other penalties resulted in images with shorter noise correlation lengths at approximately matched contrast and noise strengths. Overall, PL reconstructions resulted in fewer background regions to be confused with tumors compared to OSEM, without compromising contrast and noise strength properties.