Statistical analysis of maximum likelihood estimator images of human brain FDG PET studies

The work presented evaluates the statistical characteristics of regional bias and expected error in reconstructions of real positron emission tomography (PET) data of human brain fluoro-deoxiglucose (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 of evaluating radioisotope uptake in regions-of-interest (ROIs) is investigated. An assessment of bias and variance in uptake measurements is carried out with simulated data. Then, by using three different transition matrices with different degrees of accuracy and a components of variance model for statistical analysis, it is shown that the characteristics obtained from real human FDG brain data are consistent with the results of the simulation studies

Quantitative Statistical Methods for Image Quality Assessment

Quantitative measures of image quality and reliability are critical for both qualitative interpretation and quantitative analysis of medical images. While, in theory, it is possible to analyze reconstructed images by means of Monte Carlo simulations using a large number of noise realizations, the associated computational burden makes this approach impractical. Additionally, this approach is less meaningful in clinical scenarios, where multiple noise realizations are generally unavailable. The practical alternative is to compute closed-form analytical expressions for image quality measures. The objective of this paper is to review statistical analysis techniques that enable us to compute two key metrics: resolution (determined from the local impulse response) and covariance. The underlying methods include fixed-point approaches, which compute these metrics at a fixed point (the unique and stable solution) independent of the iterative algorithm employed, and iteration-based approaches, which yield results that are dependent on the algorithm, initialization, and number of iterations. We also explore extensions of some of these methods to a range of special contexts, including dynamic and motion-compensated image reconstruction. While most of the discussed techniques were developed for emission tomography, the general methods are extensible to other imaging modalities as well. In addition to enabling image characterization, these analysis techniques allow us to control and enhance imaging system performance. We review practical applications where performance improvement is achieved by applying these ideas to the contexts of both hardware (optimizing scanner design) and image reconstruction (designing regularization functions that produce uniform resolution or maximize task-specific figures of merit)

Development of Spect and Ct Tomographic Image Reconstruction

The purpose of this study was to contribute to the advancement of statistically-based iterative reconstruction algorithms and protocols for both SPECT and micro CT data. Major contributions of this work to SPECT reconstruction include formulation and implementation of fully three-dimensional voxel-based system matrix in parallel-beam, fan-beam, and cone-beam collimator geometries while modeling the process of attenuation, system resolution and sensitivity. This is achieved by casting rays through a volume of voxels and using ray-voxel intersection lengths to determine approximate volume contributions. Qualitative and quantitative analysis of reconstructed Monte Carlo data sets show that this is a very effective and efficient method. Using this method, three SPECT studies were conducted. First, the reconstruction performance was studied for a triple-head cone-beam SPECT system using a helical orbit acquisition. We looked at various subset groupings for the ordered-subsets expectation maximization (OSEM) algorithm. We also examined how rotational and translational sampling affects reconstructed image quality when constrained by total injected dose and scan time. We conclude the following: When reconstructing noiseless datasets, varying the rotational sampling from 90 views to 360 views over 360 degrees does not affect the reconstructed activity regardless of the object size in terms of both convergence and accuracy. When using ordered subsets, the subset group arrangement is important in terms of both image quality and accuracy. The smaller the object is that is being reconstructed, the rate of convergence decreases, the spatial resolution decreases, and accuracy decreases. Second, we examined a system composed of three, possibly different, converging collimators using a circular orbit. We conclude the following: When reconstructing noiseless datasets, using a triple-cone beam system resulted in distortion artifacts along the axial direction and diminished resolution along the transaxial direction. Using a triple-fan beam system resulted in the best reconstructed image quality in terms of bias, noise, and contrast. When noisy datasets were reconstructed, a cone-cone-fan beam system resulted in best reconstructed image quality in terms of mean-to-actual ratio for small lesions and a triple-fan beam system for large lesions. Finally, a two-dimensional mesh-based system matrix for parallel-beam collimation with attenuation and resolution modeling was designed, implemented, and studied. We conclude that no more than two divisions per detector bin width are needed for satisfactory reconstruction. Also, using more than two divisions per detector bin does not significantly improve reconstructed images. A chapter on iterative micro-CT reconstruction is also included. Our contribution to micro-CT reconstruction is the formulation and implementation of a cone-beam system matrix that reduces ring artifacts associated with sampling of the reconstruction space. This new approach reduces the common 3 D ray-tracing technique into 2-D, making it very efficient. The images obtained using our approach are compared to images reconstructed by means of analytical techniques. We observe significant improvement in image quality for the images reconstructed using our iterative method

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

Anwendung von Maximum-Likelihood Expectation-Maximization und Origin Ensemble zur Rekonstruktion von Aktivitätsverteilungen beim Single Plane Compton Imaging (SPCI)

In der nuklearmedizinischen Bildgebung mit Anger-Kameras wird ein höheres Auflösungsvermögen durch Limitierung der Nachweiseffizienz erreicht. Compton Cameras können die Nachweiseffizienz mittels elektronischer Kollimation, die zur Ortsbestimmung die Compton-Kinematik anwendet, erhöhen. Ein alternativer Ansatz für die Konstruktion einer Compton Camera, die Streu- und Absorptionsebenen in einer Ebene kombiniert, wurde in der Vergangenheit untersucht. Die sogenannte Single Plane Compton Camera ist in der Lage, Punktquellen im Vakuum getrennt aufzulösen. Zur Darstellung komplexerer Bildinhalte wird die Optimierung der Bildrekonstruktion angestrebt. Diese umfasst ein umfängliches Verständnis des Messprinzips, das in dieser Arbeit dargelegt wird. Jeweils ein 3D-Rekonstruktionsalgorithmus wurde für konventionell gebinnte und List-Mode-Daten implementiert. Anhand eines vorliegenden Simulationsdatensatzes einer einfachen Detektorkonfiguration wurden Messdaten generiert und rekonstruiert. Es konnte gezeigt werden, dass aufgrund der hohen Zählstatistik ein robustes Signal-to-Noise-Ratio erhalten wird. List-Mode-Verfahren eignen sich aufgrund eines höheren Rechenaufwandes nicht. Die mittlere Ortsinformation der Ereignisse ist systembedingt gering und beeinträchtigt die Ortsauflösung, welche für E = 662 keV etwa 15 mm in einem Abstand von 50cmm beträgt. Eine Verbesserung der Auflösung ist durch die Algorithmen nicht möglich, sondern umfasst technische Maßnahmen, welche anhand dieser Arbeit in weiteren Studien umgesetzt werden können.:1 Einleitung 2 Single Plane Compton Imaging 3 Bildrekonstruktion beim Single Plane Compton Imaging 4 Materialien und Methoden 5 Ergebnisse 6 Diskussion 7 Zusammenfassung und Ausblick Literaturverzeichnis Abkürzungsverzeichnis Abbildungsverzeichnis Tabellenverzeichnis Selbstständigkeitserklärung A Herleitung des ML-EM Algorithmus B Tiefergehende Informationen zu OE C C++-Code für die Bildrekonstruktion beim SPCIIn nuclear medicine imaging, the Anger camera imposes a limit on the detection efficiency in order to improve the spatial resolution. The detection efficiency can be increased with electronically collimated systems known as Compton Cameras, which use the kinematics of Compton scattering to locate the detected events. An alternative approach to the design of a Compton Camera combining scatter and absorption planes was investigated in the past. It was shown that the so-called Single Plane Compton Camera is able to separately reconstruct two point sources in empty space. Further optimization is required to reconstruct more complex images. Thus, an extensive understanding of the measurement principle is provided. Two 3D-algorithms were implemented for binned data and list mode data. Measurement data were generated by means of an existing simulated data set of a simple detector design and reconstructed. It is shown that a robust signal-to-noise ratio can be achieved due to high numbers of detected counts. List mode algorithms produce high computational costs and binned algorithms may be used instead. The average position information is low and imposes a negative impact on the spatial resolution, which is about 15mm at a distance of 50mm for E = 662 keV. The implemented algorithms cannot increase the spatial resolution due to lack of precise position information. Therefore, future studies should focus on technical measures, which are given in this thesis.:1 Einleitung 2 Single Plane Compton Imaging 3 Bildrekonstruktion beim Single Plane Compton Imaging 4 Materialien und Methoden 5 Ergebnisse 6 Diskussion 7 Zusammenfassung und Ausblick Literaturverzeichnis Abkürzungsverzeichnis Abbildungsverzeichnis Tabellenverzeichnis Selbstständigkeitserklärung A Herleitung des ML-EM Algorithmus B Tiefergehende Informationen zu OE C C++-Code für die Bildrekonstruktion beim SPC

Statistical analysis of maximum likelihood estimator images of human brain FDG PET studies

The work presented evaluates the statistical characteristics of regional bias and expected error in reconstructions of real positron emission tomography (PET) data of human brain fluoro-deoxiglucose (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 of evaluating radioisotope uptake in regions-of-interest (ROIs) is investigated. An assessment of bias and variance in uptake measurements is carried out with simulated data. Then, by using three different transition matrices with different degrees of accuracy and a components of variance model for statistical analysis, it is shown that the characteristics obtained from real human FDG brain data are consistent with the results of the simulation studies

Improved Modeling and Image Generation for Fluorescence Molecular Tomography (FMT) and Positron Emission Tomography (PET)

In this thesis, we aim to improve quantitative medical imaging with advanced image generation algorithms. We focus on two specific imaging modalities: fluorescence molecular tomography (FMT) and positron emission tomography (PET). For FMT, we present a novel photon propagation model for its forward model, and in addition, we propose and investigate a reconstruction algorithm for its inverse problem. In the first part, we develop a novel Neumann-series-based radiative transfer equation (RTE) that incorporates reflection boundary conditions in the model. In addition, we propose a novel reconstruction technique for diffuse optical imaging that incorporates this Neumann-series-based RTE as forward model. The proposed model is assessed using a simulated 3D diffuse optical imaging setup, and the results demonstrate the importance of considering photon reflection at boundaries when performing photon propagation modeling. In the second part, we propose a statistical reconstruction algorithm for FMT. The algorithm is based on sparsity-initialized maximum-likelihood expectation maximization (MLEM), taking into account the Poisson nature of data in FMT and the sparse nature of images. The proposed method is compared with a pure sparse reconstruction method as well as a uniform-initialized MLEM reconstruction method. Results indicate the proposed method is more robust to noise and shows improved qualitative and quantitative performance. For PET, we present an MRI-guided partial volume correction algorithm for brain imaging, aiming to recover qualitative and quantitative loss due to the limited resolution of PET system, while keeping image noise at a low level. The proposed method is based on an iterative deconvolution model with regularization using parallel level sets. A non-smooth optimization algorithm is developed so that the proposed method can be feasibly applied for 3D images and avoid additional blurring caused by conventional smooth optimization process. We evaluate the proposed method using both simulation data and in vivo human data collected from the Baltimore Longitudinal Study of Aging (BLSA). Our proposed method is shown to generate images with reduced noise and improved structure details, as well as increased number of statistically significant voxels in study of aging. Results demonstrate our method has promise to provide superior performance in clinical imaging scenarios

3D Volumetric Reconstruction for Light-Field SPECT

Preclinical research on single-photon emission computed tomography (SPECT) imaging is now well acknowledged for its critical role. It is fundamental for functional imaging and is a well-researched area of nuclear medicine emission tomography. Numerous efforts were made to provide an optimized SPECT collimator and detector design. However, these approaches suffer from limited sensitivity and resolution, demanding an efficient reconstruction algorithm development. Moreover, due to the image deterioration induced by the non-stationary collimator-detector response and the single-photon emitting nature of SPECT, it is difficult to quantify the 3D radiopharmaceutical distribution within the patient quantitatively. This dissertation's primary incentive is to design and develop a complete computational framework for the newly proposed L-SPECT scan procedure from the image acquisition to the image reconstruction. Using this framework, I solve several challenging problems related to implementing a dedicated novel 3D L-SPECT image reconstruction algorithm. In particular, a volumetric reconstruction algorithm for L-SPECT system is developed by considering the system configurations. Also, an in-depth analysis of the SPECT imaging system based on the light field concept using the micro pinhole range collimator is presented in this thesis. Moreover, I evaluate the performance of the developed reconstruction algorithms under various imaging circumstances in terms of image quality, computational complexity, and resolution. A Monte Carlo simulation environment for L-SPECT was developed by modelling the properties of the SPECT imaging setup. By examining the existing limitations in the proposed L-SPECT, an improved collimator-detector geometry for the micro-pinhole arrays was introduced in this thesis as one of the main contributions. The modular L-SPECT with the detector heads in a partial ring geometry achieved higher sensitivity and resolution than the planer L-SPECT. The modular L-SPECT was further improved by shifting the centre of the scanning detectors to eliminate the artifacts in the reconstructed images. A dedicated reconstruction algorithm for the modular L-SPECT was developed as proof of concept. In SPECT reconstruction, identification of uncertainty information would help to enhance and mitigate the limitations of the existing reconstruction algorithms. The critical contribution of this thesis is manifested in the development of an image reconstruction algorithm based on Bayesian probabilistic programming for SPECT and L-SPECT. A NUTS based MCMC algorithm is used for probabilistic programming-based reconstruction. The uncertainty associated with the radiation measurement is identified as a distribution from the posterior samples generated using the MCMC algorithm. The performance of the NUTS algorithm improved by using reverse-mode automatic differentiation and distributed programming. The automatic differentiation variational inference-based SPECT reconstruction algorithm is developed to reduce the computational cost in NUTS based reconstruction and uncertainty analysis. Further in this thesis, the L-SPECT simulations are calibrated by comparing with GATE simulations, which are the gold standard in this field. The projection results of MATLAB based simulations are comparable with GATE simulations. The system performance for the proposed different configurations was investigated and contrasted against the existing SPECT modalities and systems, such as LEHR and Inveon SPECT, respectively. The performance analysis of the L-SPECT revealed the system is able to achieve improved sensitivity and better field of view compared to the existing systems. The essential characteristics of this L-SPECT system based on the reconstructed images were assessed with pinhole radii of 0.1 mm and 0.05 mm. In addition, the system sensitivity, spatial resolution, and image quality are appraised from the 3D reconstructed images. The maximum achieved system’s sensitivity was 1000 Cps/Bbq using arrays with a pinhole radius of 0.1 mm at 1 mm pitch, while the highest resolution was obtained using arrays with 0.05 mm pinhole and 3 mm pitch. The designed L-SPECT with different configurations and the developed 3D reconstruction algorithms yielded superior image quality compared with LEHR reconstructions

Incorporating accurate statistical modeling in PET: reconstruction for whole-body imaging

Tese de doutoramento em Biofísica, apresentada à Universidade de Lisboa através da Faculdade de Ciências, 2007The thesis is devoted to image reconstruction in 3D whole-body PET imaging. OSEM ( Ordered Subsets Expectation maximization ) is a statistical algorithm that assumes Poisson data. However, corrections for physical effects (attenuation, scattered and random coincidences) and detector efficiency remove the Poisson characteristics of these data. The Fourier Rebinning (FORE), that combines 3D imaging with fast 2D reconstructions, requires corrected data. Thus, if it will be used or whenever data are corrected prior to OSEM, the need to restore the Poisson-like characteristics is present. Restoring Poisson-like data, i.e., making the variance equal to the mean, was achieved through the use of weighted OSEM algorithms. One of them is the NECOSEM, relying on the NEC weighting transformation. The distinctive feature of this algorithm is the NEC multiplicative factor, defined as the ratio between the mean and the variance. With real clinical data this is critical, since there is only one value collected for each bin the data value itself. For simulated data, if we keep track of the values for these two statistical moments, the exact values for the NEC weights can be calculated. We have compared the performance of five different weighted algorithms (FORE+AWOSEM, FORE+NECOSEM, ANWOSEM3D, SPOSEM3D and NECOSEM3D) on the basis of tumor detectablity. The comparison was done for simulated and clinical data. In the former case an analytical simulator was used. This is the ideal situation, since all the weighting factors can be exactly determined. For comparing the performance of the algorithms, we used the Non-Prewhitening Matched Filter (NPWMF) numerical observer. With some knowledge obtained from the simulation study we proceeded to the reconstruction of clinical data. In that case, it was necessary to devise a strategy for estimating the NEC weighting factors. The comparison between reconstructed images was done by a physician largely familiar with whole-body PET imaging