Direct estimation of kinetic parametric images for dynamic PET.

Dynamic positron emission tomography (PET) can monitor spatiotemporal distribution of radiotracer in vivo. The spatiotemporal information can be used to estimate parametric images of radiotracer kinetics that are of physiological and biochemical interests. Direct estimation of parametric images from raw projection data allows accurate noise modeling and has been shown to offer better image quality than conventional indirect methods, which reconstruct a sequence of PET images first and then perform tracer kinetic modeling pixel-by-pixel. Direct reconstruction of parametric images has gained increasing interests with the advances in computing hardware. Many direct reconstruction algorithms have been developed for different kinetic models. In this paper we review the recent progress in the development of direct reconstruction algorithms for parametric image estimation. Algorithms for linear and nonlinear kinetic models are described and their properties are discussed

Monte-Carlo simulations and image reconstruction for novel imaging scenarios in emission tomography

AbstractEmission imaging incorporates both the development of dedicated devices for data acquisition as well as algorithms for recovering images from that data. Emission tomography is an indirect approach to imaging. The effect of device modification on the final image can be understood through both the way in which data are gathered, using simulation, and the way in which the image is formed from that data, or image reconstruction. When developing novel devices, systems and imaging tasks, accurate simulation and image reconstruction allow performance to be estimated, and in some cases optimized, using computational methods before or during the process of physical construction. However, there are a vast range of approaches, algorithms and pre-existing computational tools that can be exploited and the choices made will affect the accuracy of the in silico results and quality of the reconstructed images. On the one hand, should important physical effects be neglected in either the simulation or reconstruction steps, specific enhancements provided by novel devices may not be represented in the results. On the other hand, over-modeling of device characteristics in either step leads to large computational overheads that can confound timely results. Here, a range of simulation methodologies and toolkits are discussed, as well as reconstruction algorithms that may be employed in emission imaging. The relative advantages and disadvantages of a range of options are highlighted using specific examples from current research scenarios

Efficient Calculation of Resolution and Covariance for Penalized-Likelihood Reconstruction in Fully 3-D SPECT

Resolution and covariance predictors have been derived previously for penalized-likelihood estimators. These predictors can provide accurate approximations to the local resolution properties and covariance functions for tomographic systems given a good estimate of the mean measurements. Although these predictors may be evaluated iteratively, circulant approximations are often made for practical computation times. However, when numerous evaluations are made repeatedly (as in penalty design or calculation of variance images), these predictors still require large amounts of computing time. In Stayman and Fessler (2000), we discussed methods for precomputing a large portion of the predictor for shift-invariant system geometries. In this paper, we generalize the efficient procedure discussed in Stayman and Fessler (2000) to shift-variant single photon emission computed tomography (SPECT) systems. This generalization relies on a new attenuation approximation and several observations on the symmetries in SPECT systems. These new general procedures apply to both two-dimensional and fully three-dimensional (3-D) SPECT models, that may be either precomputed and stored, or written in procedural form. We demonstrate the high accuracy of the predictions based on these methods using a simulated anthropomorphic phantom and fully 3-D SPECT system. The evaluation of these predictors requires significantly less computation time than traditional prediction techniques, once the system geometry specific precomputations have been made.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85992/1/Fessler54.pd

Four-dimensional tomographic reconstruction by time domain decomposition

Since the beginnings of tomography, the requirement that the sample does not change during the acquisition of one tomographic rotation is unchanged. We derived and successfully implemented a tomographic reconstruction method which relaxes this decades-old requirement of static samples. In the presented method, dynamic tomographic data sets are decomposed in the temporal domain using basis functions and deploying an L1 regularization technique where the penalty factor is taken for spatial and temporal derivatives. We implemented the iterative algorithm for solving the regularization problem on modern GPU systems to demonstrate its practical use

Conjugate-Gradient Preconditioning Methods for Shift-Variant PET Image Reconstruction

Gradient-based iterative methods often converge slowly for tomographic image reconstruction and image restoration problems, but can be accelerated by suitable preconditioners. Diagonal preconditioners offer some improvement in convergence rate, but do not incorporate the structure of the Hessian matrices in imaging problems. Circulant preconditioners can provide remarkable acceleration for inverse problems that are approximately shift-invariant, i.e., for those with approximately block-Toeplitz or block-circulant Hessians. However, in applications with nonuniform noise variance, such as arises from Poisson statistics in emission tomography and in quantum-limited optical imaging, the Hessian of the weighted least-squares objective function is quite shift-variant, and circulant preconditioners perform poorly. Additional shift-variance is caused by edge-preserving regularization methods based on nonquadratic penalty functions. This paper describes new preconditioners that approximate more accurately the Hessian matrices of shift-variant imaging problems. Compared to diagonal or circulant preconditioning, the new preconditioners lead to significantly faster convergence rates for the unconstrained conjugate-gradient (CG) iteration. We also propose a new efficient method for the line-search step required by CG methods. Applications to positron emission tomography (PET) illustrate the method.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85979/1/Fessler85.pd

4-D Tomographic Inference: Application to SPECT and MR-driven PET

Emission tomographic imaging is framed in the Bayesian and information theoretic framework. The first part of the thesis is inspired by the new possibilities offered by PET-MR systems, formulating models and algorithms for 4-D tomography and for the integration of information from multiple imaging modalities. The second part of the thesis extends the models described in the first part, focusing on the imaging hardware. Three key aspects for the design of new imaging systems are investigated: criteria and efficient algorithms for the optimisation and real-time adaptation of the parameters of the imaging hardware; learning the characteristics of the imaging hardware; exploiting the rich information provided by depthof- interaction (DOI) and energy resolving devices. The document concludes with the description of the NiftyRec software toolkit, developed to enable 4-D multi-modal tomographic inference

Topics in image reconstruction for high resolution positron emission tomography

Les problèmes mal posés représentent un sujet d'intérêt interdisciplinaire qui surgires dans la télédétection et des applications d'imagerie. Cependant, il subsiste des questions cruciales pour l'application réussie de la théorie à une modalité d'imagerie. La tomographie d'émission par positron (TEP) est une technique d'imagerie non-invasive qui permet d'évaluer des processus biochimiques se déroulant à l'intérieur d'organismes in vivo. La TEP est un outil avantageux pour la recherche sur la physiologie normale chez l'humain ou l'animal, pour le diagnostic et le suivi thérapeutique du cancer, et l'étude des pathologies dans le coeur et dans le cerveau. La TEP partage plusieurs similarités avec d'autres modalités d'imagerie tomographiques, mais pour exploiter pleinement sa capacité à extraire le maximum d'information à partir des projections, la TEP doit utiliser des algorithmes de reconstruction d'images à la fois sophistiquée et pratiques. Plusieurs aspects de la reconstruction d'images TEP ont été explorés dans le présent travail. Les contributions suivantes sont d'objet de ce travail: Un modèle viable de la matrice de transition du système a été élaboré, utilisant la fonction de réponse analytique des détecteurs basée sur l'atténuation linéaire des rayons y dans un banc de détecteur. Nous avons aussi démontré que l'utilisation d'un modèle simplifié pour le calcul de la matrice du système conduit à des artefacts dans l'image. (IEEE Trans. Nucl. Sei., 2000) );> La modélisation analytique de la dépendance décrite à l'égard de la statistique des images a simplifié l'utilisation de la règle d'arrêt par contre-vérification (CV) et a permis d'accélérer la reconstruction statistique itérative. Cette règle peut être utilisée au lieu du procédé CV original pour des projections aux taux de comptage élevés, lorsque la règle CV produit des images raisonnablement précises. (IEEE Trans. Nucl. Sei., 2001) Nous avons proposé une méthodologie de régularisation utilisant la décomposition en valeur propre (DVP) de la matrice du système basée sur l'analyse de la résolution spatiale. L'analyse des caractéristiques du spectre de valeurs propres nous a permis d'identifier la relation qui existe entre le niveau optimal de troncation du spectre pour la reconstruction DVP et la résolution optimale dans l'image reconstruite. (IEEE Trans. Nucl. Sei., 2001) Nous avons proposé une nouvelle technique linéaire de reconstruction d'image événement-par-événement basée sur la matrice pseudo-inverse régularisée du système. L'algorithme représente une façon rapide de mettre à jour une image, potentiellement en temps réel, et permet, en principe, la visualisation instantanée de distribution de la radioactivité durant l'acquisition des données tomographiques. L'image ainsi calculée est la solution minimisant les moindres carrés du problème inverse régularisé.Abstract: Ill-posed problems are a topic of an interdisciplinary interest arising in remote sensing and non-invasive imaging. However, there are issues crucial for successful application of the theory to a given imaging modality. Positron emission tomography (PET) is a non-invasive imaging technique that allows assessing biochemical processes taking place in an organism in vivo. PET is a valuable tool in investigation of normal human or animal physiology, diagnosing and staging cancer, heart and brain disorders. PET is similar to other tomographie imaging techniques in many ways, but to reach its full potential and to extract maximum information from projection data, PET has to use accurate, yet practical, image reconstruction algorithms. Several topics related to PET image reconstruction have been explored in the present dissertation. The following contributions have been made: (1) A system matrix model has been developed using an analytic detector response function based on linear attenuation of [gamma]-rays in a detector array. It has been demonstrated that the use of an oversimplified system model for the computation of a system matrix results in image artefacts. (IEEE Trans. Nucl. Sci., 2000); (2) The dependence on total counts modelled analytically was used to simplify utilisation of the cross-validation (CV) stopping rule and accelerate statistical iterative reconstruction. It can be utilised instead of the original CV procedure for high-count projection data, when the CV yields reasonably accurate images. (IEEE Trans. Nucl. Sci., 2001); (3) A regularisation methodology employing singular value decomposition (SVD) of the system matrix was proposed based on the spatial resolution analysis. A characteristic property of the singular value spectrum shape was found that revealed a relationship between the optimal truncation level to be used with the truncated SVD reconstruction and the optimal reconstructed image resolution. (IEEE Trans. Nucl. Sci., 2001); (4) A novel event-by-event linear image reconstruction technique based on a regularised pseudo-inverse of the system matrix was proposed. The algorithm provides a fast way to update an image potentially in real time and allows, in principle, for the instant visualisation of the radioactivity distribution while the object is still being scanned. The computed image estimate is the minimum-norm least-squares solution of the regularised inverse problem