Calvin A. Johnson

Design of a motion-compensation OSEM list-mode algorithm for resolution-recovery reconstruction for the HRRT

The HRRT PET system has the potential to produce human brain images with resolution better than 3 mm. To achieve the best possible accuracy and precision, we have designed MOLAR, a motion-compensation OSEM list-mode algorithm for resolution-recovery reconstruction on a computer cluster with the following features: direct use of list mode data with dynamic motion information (Polaris); exact reprojection of each line-of- response (LOR); system matrix computed from voxel-to-LOR distances (radial and axial); spatially varying resolution model implemented for each event by selection from precomputed line spread functions based on factors including detector obliqueness, crystal layer, and block detector position; distribution of events to processors and to subsets based on order of arrival; removal of voxels and events outside a reduced field-of-view defined by the attenuation map; no pre-corrections to Poisson data, i.e., all physical effects are defined in the model; randoms estimation from singles; model-based scatter simulation incorporated into the iterations; and component-based normalization. Preliminary computation estimates suggest that reconstruction of a single frame in one hour is achievable. Careful evaluation of this system will define which factors play an important role in producing high resolution, low-noise images with quantitative accuracy.

A system for the 3D reconstruction of retracted-septa PET data using the EM algorithm

We have implemented the EM reconstruction algorithm for volume acquisition from current generation retracted-septa PET scanners. Although the software was designed for a GE Advance scanner, it is easily adaptable to other 3D scanners. The reconstruction software was written for an Intel iPSC/860 parallel computer with 128 compute nodes. Running on 32 processors, the algorithm requires approximately 55 minutes per iteration to reconstruct a 128/spl times/128/spl times/35 image. No projection data compression schemes or other approximations were used in the implementation. Extensive use of EM system matrix (C/sub ij/) symmetries (including the 8-fold in-plane symmetries, 2-fold axial symmetries, and axial parallel line redundancies) reduces the storage cost by a factor of 188. The parallel algorithm operates on distributed projection data which are decomposed by base-symmetry angles. Symmetry operators copy and index the C/sub ij/ chord to the form required for the particular symmetry. The use of asynchronous reads, lookup tables, and optimized image indexing improves computational performance. >

Evaluation of 3D reconstruction algorithms for a small animal PET camera

The use of paired, opposing position-sensitive phototube scintillation cameras (SCs) operating in coincidence for small animal imaging with positron emitters is currently under study. Because of the low sensitivity of the system even in 3D mode and the need to produce images with high resolution, it was postulated that a 3D expectation maximization (EM) reconstruction algorithm might be well suited for this application. We investigated four reconstruction algorithms for the 3D SC PET camera: 2D filtered back-projection (FBP), 2D ordered subset EM (OSEM), 3D reprojection (3DRP), and 3D OSEM. Noise was assessed for all slices by the coefficient of variation in a simulated uniform cylinder. Resolution was assessed from a simulation of 15 point sources in the warm background of the uniform cylinder. At comparable noise levels, the resolution achieved with OSEM (0.9-mm to 1.2-mm) is significantly better than that obtained with FBP or 3DRP (1.5-mm to 2.0-mm.) Images of a rat skull labeled with /sup 18/F-fluoride suggest that 3D OSEM can improve image quality of a small animal PET camera.

Performance characteristics of the 3-D OSEM algorithm in the reconstruction of small animal PET images

Rat brain images acquired with a small animal positron emission tomography (PET) camera and reconstructed with the three-dimensional (3-D) ordered-subsets expectation-maximization (OSEM) algorithm with resolution recovery have better quality when the brain is imaged by itself than when inside the head with surrounding background activity. The purpose of this study was to characterize the dependence of this effect on the level of background activity, attenuation, and scatter. Monte Carlo simulations of the imaging system were performed. The coefficient of variation from replicate images, full-width at half-maximum (FWHM) from point sources and image profile fitting, and image contrast and uniformity were used to evaluate algorithm performance. A rat head with the typical levels of five and ten times the brain activity in the surrounding background requires additional iterations to achieve the same resolution as the brain-only case at a cost of 24% and 64% additional noise, respectively. For the same phantoms, object scatter reduced contrast by 3%-5%. However, attenuation degraded resolution by 0.2 mm and was responsible for up to 12% nonuniformity in the brain images suggesting that attenuation correction is useful. Given the effects of emission and attenuation distribution on both resolution and noise, simulations or phantom studies should be used for each imaging situation to select the appropriate number of OSEM iterations to achieve the desired resolution-noise levels.

Interior-point methodology for 3-D PET reconstruction

Interior-point methods have been successfully applied to a wide variety of linear and nonlinear programming applications. This paper presents a class of algorithms, based on path-following interior-point methodology, for performing regularized maximum-likelihood (ML) reconstructions on three-dimensional (3-D) emission tomography data. The algorithms solve a sequence of subproblems that converge to the regularized maximum likelihood solution from the interior of the feasible region (the nonnegative orthant). The authors propose two methods, a primal method which updates only the primal image variables and a primal-dual method which simultaneously updates the primal variables and the Lagrange multipliers. A parallel implementation permits the interior-point methods to scale to very large reconstruction problems. Termination is based on well-defined convergence measures, namely, the Karush-Kuhn-Tucker first-order necessary conditions for optimality. The authors demonstrate the rapid convergence of the path-following interior-point methods using both data from a small animal scanner and Monte Carlo simulated data. The proposed methods can readily be applied to solve the regularized, weighted least squares reconstruction problem.

A data-parallel algorithm for iterative tomographic image reconstruction

In the tomographic imaging problem images are reconstructed from a set of measured projections. Iterative reconstruction methods are computationally intensive alternatives to the more traditional Fourier-based methods. Despite their high cost, the popularity of these methods is increasing because of the advantages they pose. Although numerous iterative methods have been proposed over the years, all of these methods can be shown to have a similar computational structure. This paper presents a parallel algorithm that we originally developed for performing the expectation maximization algorithm in emission tomography. This algorithm is capable of exploiting the sparsity and symmetries of the model in a computationally efficient manner. Our parallelization scheme is based upon decomposition of the measurement-space vectors. We demonstrate that such a parallelization scheme is applicable to the vast majority of iterative reconstruction algorithms proposed to date.

Count-Rate Dependent Component-Based Normalization for the HRRT

Component-based normalization is an important technique for PET scanners with a high number of lines of response (LOR), e.g., 4.5 times 109 for the HRRT. It reduces the problem of measuring the sensitivity of each LOR to that of estimating the individual crystal efficiencies(epsiv), e.g., 119808 for the HRRT. We propose a component-based method to compute epsiv for the HRRT. In addition, the block design of the HRRT produces pulse pile-up which causes apparent changes in epsiv 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 values and a decaying uniform phantom to account for variations with count rate. The computation of efficiencies is achieved with ~1% statistical noise with an acquisition of ~1 h. Count rate dependency of epsiv is implemented as a linear model in terms of block singles rate. Four approaches to modify epsiv 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 epsiv leads to high resolution artifacts in the reconstructed images, most visible in the transverse plane, in the center of the field-of-view.

Delineation of a conserved arrestin-biased signaling repertoire in vivo.

Biased G protein–coupled receptor agonists engender a restricted repertoire of downstream events from their cognate receptors, permitting them to produce mixed agonist-antagonist effects in vivo. While this opens the possibility of novel therapeutics, it complicates rational drug design, since the in vivo response to a biased agonist cannot be reliably predicted from its in cellula efficacy. We have employed novel informatic approaches to characterize the in vivo transcriptomic signature of the arrestin pathway-selective parathyroid hormone analog [d-Trp12, Tyr34]bovine PTH(7-34) in six different murine tissues after chronic drug exposure. We find that [d-Trp12, Tyr34]bovine PTH(7-34) elicits a distinctive arrestin-signaling focused transcriptomic response that is more coherently regulated across tissues than that of the pluripotent agonist, human PTH(1-34). This arrestin-focused network is closely associated with transcriptional control of cell growth and development. Our demonstration of a conserved arrestin-dependent transcriptomic signature suggests a framework within which the in vivo outcomes of arrestin-biased signaling may be generalized.

Maximum entropy reconstruction methods in electron paramagnetic resonance imaging

Electron Paramagnetic Resonance (EPR) is a spectroscopic technique that detects and characterizes molecules with unpaired electrons (i.e., free radicals). Unlike the closely related nuclear magnetic resonance (NMR) spectroscopy, EPR is still under development as an imaging modality. Athough a number of physical factors have hindered its development, EPRs potential is quite promising in a number of important application areas, including in vivo oximetry. EPR images are generally reconstructed using a tomographic imaging technique, of which filtered backprojection (FBP) is the most commonly used. We apply two iterative methods for maximum-entropy image reconstruction in EPR. The first is the multiplicative algebraic reconstruction technique (MART), a well-known row-action method. We propose a second method, known as LSEnt (least-squares entropy), that maximizes entropy and performs regularization by maintaining a desired distance from the measurements. LSEnt is in part motivated by the barrier method of interior-point programming. We present studies in which images of two physical phantoms, reconstructed using FBP, MART, and LSEnt, are compared. The images reconstructed using MART and LSEnt have lower variance, better contrast recovery, subjectively better resolution, and reduced streaking artifact than those reconstructed using FBP. These results suggest that maximum-entropy reconstruction methods (particularly the more flexible LSEnt) may be critical in overcoming some of the physical challenges of EPR imaging.

A Primal-Dual Method for Large-Scale Image Reconstruction in Emission Tomography

In emission tomography, images can be reconstructed from a set of measured projections using a maximum likelihood (ML) criterion. In this paper, we present a primal-dual algorithm for large-scale three-dimensional image reconstruction. The primal-dual method is specialized to the ML reconstruction problem. The reconstruction problem is extremely large; in several of our data sets the Hessian of the objective function is the product of a 1.4 million by 63 million matrix and its scaled transpose. As such, we consider only approaches that are suitable for large-scale parallel computation. We apply a stabilization technique to the system of equations for computing the primal direction and demonstrate the need for stabilization when approximately solving the system using an early-terminated conjugate gradient iteration. We demonstrate that the primal-dual method for this problem converges faster than the logarithmic barrier method and considerably faster than the expectation maximization algorithm. The use of extrapolation in conjunction with the primal-dual method further reduces the overall computation required to achieve convergence.