Validation of 3D Model-Based Maximum-Likelihood Estimation of Normalisation Factors for Partial Ring Positron Emission Tomography

The next generation of organ specific Positron Emission Tomography (PET) scanners, e.g. for breast imaging, will use partial ring geometries. We propose a component-based Maximum-Likelihood (ML) estimation of normalisation factors for 3D PET data reconstruction applicable to partial ring geometries. This method is based on the Software for Tomographic Image Reconstruction (STIR) for full ring PET and is validated for a stationary partial ring scanner. The model includes the estimation for crystal efficiencies and geometric factors. The algorithm is validated using Maximum Likelihood Estimation Method (MLEM) based 3D reconstruction in STIR using Geant4 Application for Tomographic Emission (GATE) simulation data for full and partial ring scanners and experimental data from a demonstrator with partial ring geometry. The uniformity of the reconstructed images of simulated cylindrical and NEMAIQ phantoms in both scanner geometries and the image of a line source in the partial ring demonstrator is assessed. The results have shown that uniform images in both axial and transaxial directions are obtained after applying the estimated normalisation factors. The accuracy of the algorithm is validated by comparing the normalisation factors between the full and partial ring systems in simulation. We have shown that the estimated normalisation factors are almost identical, even though the separate components are not. This proves that the ML estimation of the 3D normalisation factors is valid and can be applied to the partial ring scanner

3D PET image reconstruction based on Maximum Likelihood Estimation Method (MLEM) algorithm

Positron emission tomographs (PET) do not measure an image directly. Instead, they measure at the boundary of the field-of-view (FOV) of PET tomograph a sinogram that consists of measurements of the sums of all the counts along the lines connecting two detectors. As there is a multitude of detectors build-in typical PET tomograph structure, there are many possible detector pairs that pertain to the measurement. The problem is how to turn this measurement into an image (this is called imaging). Decisive improvement in PET image quality was reached with the introduction of iterative reconstruction techniques. This stage was reached already twenty years ago (with the advent of new powerful computing processors). However, three dimensional (3D) imaging remains still a challenge. The purpose of the image reconstruction algorithm is to process this imperfect count data for a large number (many millions) of lines-of-responce (LOR) and millions of detected photons to produce an image showing the distribution of the labeled molecules in space.Comment: 10 pages, 7 figure

Development of methods for time efficient scatter correction and improved attenuation correction in time-of-flight PET/MR

In der vorliegenden Dissertation wurden zwei fortdauernde Probleme der Bildrekonstruktion in der time-of-flight (TOF) PET bearbeitet: Beschleunigung der TOF-Streukorrektur sowie Verbesserung der emissionsbasierten Schwächungskorrektur. Aufgrund der fehlenden Möglichkeit, die Photonenabschwächung direkt zu messen, ist eine Verbesserung der Schwächungskorrektur durch eine gemeinsame Rekonstruktion der Aktivitäts- und Schwächungskoeffizienten-Verteilung mittels der MLAA-Methode von besonderer Bedeutung für die PET/MRT, während eine Beschleunigung der TOF-Streukorrektur gleichermaßen auch für TOF-fähige PET/CT-Systeme relevant ist. Für das Erreichen dieser Ziele wurde in einem ersten Schritt die hochauflösende PET-Bildrekonstruktion THOR, die bereits zuvor in unserer Gruppe entwickelt wurde, angepasst, um die TOF-Information nutzen zu können, welche von allen modernen PET-Systemen zur Verfügung gestellt wird. Die Nutzung der TOF-Information in der Bildrekonstruktion führt zu reduziertem Bildrauschen und zu einer verbesserten Konvergenzgeschwindigkeit. Basierend auf diesen Anpassungen werden in der vorliegenden Arbeit neue Entwicklungen für eine Verbesserung der TOF-Streukorrektur und der MLAA-Rekonstruktion beschrieben. Es werden sodann Ergebnisse vorgestellt, welche mit den neuen Algorithmen am Philips Ingenuity PET/MRT-Gerät erzielt wurden, das gemeinsam vom Helmholtz-Zentrum Dresden-Rossendorf (HZDR) und dem Universitätsklinikum betrieben wird. Eine wesentliche Voraussetzung für eine quantitative TOF-Bildrekonstruktionen ist eine Streukorrektur, welche die TOF-Information mit einbezieht. Die derzeit übliche Referenzmethode hierfür ist eine TOF-Erweiterung des single scatter simulation Ansatzes (TOF-SSS). Diese Methode wurde im Rahmen der TOF-Erweiterung von THOR implementiert. Der größte Nachteil der TOF-SSS ist eine 3–7-fach erhöhte Rechenzeit für die Berechnung der Streuschätzung im Vergleich zur non-TOF-SSS, wodurch die Bildrekonstruktionsdauer deutlich erhöht wird. Um dieses Problem zu beheben, wurde eine neue, schnellere TOF-Streukorrektur (ISA) entwickelt und implementiert. Es konnte gezeigt werden, dass dieser neue Algorithmus eine brauchbare Alternative zur TOF-SSS darstellt, welche die Rechenzeit auf ein Fünftel reduziert, wobei mithilfe von ISA und TOF-SSS rekonstruierte Schnittbilder quantitativ ausgezeichnet übereinstimmen. Die Gesamtrekonstruktionszeit konnte mithilfe ISA bei Ganzkörperuntersuchungen insgesamt um den Faktor Zwei reduziert werden. Dies kann als maßgeblicher Fortschritt betrachtet werden, speziell im Hinblick auf die Nutzung fortgeschrittener Bildrekonstruktionsverfahren im klinischen Umfeld. Das zweite große Thema dieser Arbeit ist ein Beitrag zur verbesserten Schwächungskorrektur in der PET/MRT mittels MLAA-Rekonstruktion. Hierfür ist zunächst eine genaue Kenntnis der tatsächlichen Zeitauflösung in der betrachten PET-Aufnahme zwingend notwendig. Da die vom Hersteller zur Verfügung gestellten Zahlen nicht immer verlässlich sind und zudem die Zählratenabhängigkeit nicht berücksichtigen, wurde ein neuer Algorithmus entwickelt und implementiert, um die Zeitauflösung in Abhängigkeit von der Zählrate zu bestimmen. Dieser Algorithmus (MLRES) basiert auf dem maximum likelihood Prinzip und erlaubt es, die funktionale Abhängigkeit der Zeitauflösung des Philips Ingenuity PET/MRT von der Zählrate zu bestimmen. In der vorliegenden Arbeit konnte insbesondere gezeigt werden, dass sich die Zeitauflösung des Ingenuity PET/MRT im klinisch relevanten Zählratenbereich um mehr als 250 ps gegenüber der vom Hersteller genannten Auflösung von 550 ps verschlechtern kann, welche tatsächlich nur bei extrem niedrigen Zählraten erreicht wird. Basierend auf den oben beschrieben Entwicklungen konnte MLAA in THOR integriert werden. Die MLAA-Implementierung erlaubt die Generierung realistischer patientenspezifischer Schwächungsbilder. Es konnte insbesondere gezeigt werden, dass auch Knochen und Hohlräume korrekt identifiziert werden, was mittels MRT-basierter Schwächungskorrektur sehr schwierig oder sogar unmöglich ist. Zudem konnten wir bestätigen, dass es mit MLAA möglich ist, metallbedingte Artefakte zu reduzieren, die ansonsten in den MRT-basierten Schwächungsbildern immer zu finden sind. Eine detaillierte Analyse der Ergebnisse zeigte allerdings verbleibende Probleme bezüglich der globalen Skalierung und des lokalen Übersprechens zwischen Aktivitäts- und Schwächungsschätzung auf. Daher werden zusätzliche Entwicklungen erforderlich sein, um auch diese Defizite zu beheben.The present work addresses two persistent issues of image reconstruction for time-of-flight (TOF) PET: acceleration of TOF scatter correction and improvement of emission-based attenuation correction. Due to the missing capability to measure photon attenuation directly, improving attenuation correction by joint reconstruction of the activity and attenuation coefficient distribution using the MLAA technique is of special relevance for PET/MR while accelerating TOF scatter correction is of equal importance for TOF-capable PET/CT systems as well. To achieve the stated goals, in a first step the high-resolution PET image reconstruction THOR, previously developed in our group, was adapted to take advantage of the TOF information delivered by state-of-the-art PET systems. TOF-aware image reconstruction reduces image noise and improves convergence rate both of which is highly desirable. Based on these adaptations, this thesis describes new developments for improvement of TOF scatter correction and MLAA reconstruction and reports results obtained with the new algorithms on the Philips Ingenuity PET/MR jointly operated by the Helmholtz-Zentrum Dresden-Rossendorf (HZDR) and the University Hospital. A crucial requirement for quantitative TOF image reconstruction is TOF-aware scatter correction. The currently accepted reference method — the TOF extension of the single scatter simulation approach (TOF-SSS) — was implemented as part of the TOF-related modifications of THOR. The major drawback of TOF-SSS is a 3–7 fold increase in computation time required for the scatter estimation, compared to regular SSS, which in turn does lead to a considerable image reconstruction slowdown. This problem was addressed by development and implementation of a novel accelerated TOF scatter correction algorithm called ISA. This new algorithm proved to be a viable alternative to TOF-SSS and speeds up scatter correction by a factor of up to five in comparison to TOF-SSS. Images reconstructed using ISA are in excellent quantitative agreement with those obtained when using TOF-SSS while overall reconstruction time is reduced by a factor of two in whole-body investigations. This can be considered a major achievement especially with regard to the use of advanced image reconstruction in a clinical context. The second major topic of this thesis is contribution to improved attenuation correction in PET/MR by utilization of MLAA reconstruction. First of all, knowledge of the actual time resolution operational in the considered PET scan is mandatory for a viable MLAA implementation. Since vendor-provided figures regarding the time resolution are not necessarily reliable and do not cover count-rate dependent effects at all, a new algorithm was developed and implemented to determine the time resolution as a function of count rate. This algorithm (MLRES) is based on the maximum likelihood principle and allows to determine the functional dependency of the time resolution of the Philips Ingenuity PET/MR on the given count rate and to integrate this information into THOR. Notably, the present work proves that the time resolution of the Ingenuity PET/MR can degrade by more than 250 ps for the clinically relevant range of count rates in comparison to the vendor-provided figure of 550 ps which is only realized in the limit of extremely low count rates. Based on the previously described developments, MLAA could be integrated into THOR. The performed list-mode MLAA implementation is capable of deriving realistic, patient-specific attenuation maps. Especially, correct identification of osseous structures and air cavities could be demonstrated which is very difficult or even impossible with MR-based approaches to attenuation correction. Moreover, we have confirmed that MLAA is capable of reducing metal-induced artifacts which are otherwise present in MR-based attenuation maps. However, the detailed analysis of the obtained MLAA results revealed remaining problems regarding stability of global scaling as well as local cross-talk between activity and attenuation estimates. Therefore, further work beyond the scope of the present work will be necessary to address these remaining issues

Patch-based image reconstruction for PET using prior-image derived dictionaries

This collection contains figures and reconstructed images in .mat format associated with the manuscript tiled "Patch-based image reconstruction for PET using prior-image derived dictionaries" . The file, Data_Fig9-10.zip contains the reconstructed images associated with Fig 9 and 10 as a function of iteration for different methods. Data_Fig10-12.zip contains reconstructed images of the real data for different methods

Spatio-temporal PET imaging reconstruction with learned diffeomorphism

openLa Tomografia ad Emissione di Positroni (PET) è una modalità di imaging medico per ricostruire la distribuzione dell’attività metabolica, che viene utilizzata per rilevare lesioni tumorali grazie alle loro peculiari impronte metaboliche. Tuttavia, poiché richiede un lungo tempo di acquisizione, è soggetta ad artefatti da movimento e ciò porta ad una difficile individuazione dei tumori di piccole dimensioni, che sono i più importanti per una diagnosi precoce. L’algoritmo Morphed Maximum Likelihood Activity and Attenuation (M-MLAA) è stato sviluppato per affrontare il problema degli artefatti da movimento sfruttando i dati suddivisi in gate e la rete neurale SynthMorph per la registrazione di immagini, al fine di ricostruire un’immagine corretta dagli artefatti di movimento. L’obiettivo di questo progetto è l’implementazione su dati clinici dell’algoritmo M-MLAA e la valutazione delle sue prestazioni; purtroppo, ciò non è stato possibile a causa di problemi nell’implementazione dell’algoritmo Maximum Likelihood Activity and Attenuation (MLAA) sulla libreria Python Synergistic Image Reconstruction Framework (SIRF). I risultati mostrano che tali problemi potrebbero essere causati da una definizione errata della trasformata di Radon nella libreria. Nonostante ciò, l’algoritmo M-MLAA mostra buone prestazioni quando testato su dati sintetici, suggerendo che potrebbe rappresentare un promettente metodo di correzione dagli artefatti di movimento nella ricostruzione di immagini PET, consentendo di individuare lesioni tumorali in fase precoce.Positron Emission Tomography (PET) is a medical imaging modality to reconstruct the distribution of metabolic activity that is used to detect cancer lesions thanks to their peculiar metabolic fingerprints. However, since it requires long acquisition time, it is affected by motion artifacts and this leads to a difficult detection of small size tumours, that are the most important for early-stage diagnosis. The Morphed Maximum Likelihood Activity and Attenuation (M-MLAA) algorithm has been developed to assess the motion artifact problem by gaining advantage of gated data and SynthMorph image registration network to reconstruct a motion corrected image. This project’s goal is to implement the M-MLAA algorithm on clinical data and to evaluate its performance; unfortunately, this was not achieved due to problems in the implementation of the Maximum Likelihood Activity and Attenuation (MLAA) algorithm on Synergistic Image Reconstruction Framework (SIRF) Python library. The results show that those problems might be caused by an incorrect definition of the Radon transform in the library. Despite that, M-MLAA algorithm shows good performances when tested on synthetic data, suggesting that it could be a promising motion correction reconstruction method for PET images, capable of detecting early-stage cancer lesions

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)

Quantitative PET image reconstruction employing nested expectation-maximization deconvolution for motion compensation

Bulk body motion may randomly occur during PET acquisitions introducing blurring, attenuation-emission mismatches and, in dynamic PET, discontinuities in the measured time activity curves between consecutive frames. Meanwhile, dynamic PET scans are longer, thus increasing the probability of bulk motion. In this study, we propose a streamlined 3D PET motion-compensated image reconstruction (3D-MCIR) framework, capable of robustly deconvolving intra-frame motion from a static or dynamic 3D sinogram. The presented 3D-MCIR methods need not partition the data into multiple gates, such as 4D MCIR algorithms, or access list-mode (LM) data, such as LM MCIR methods, both associated with increased computation or memory resources. The proposed algorithms can support compensation for any periodic and non-periodic motion, such as cardio-respiratory or bulk motion, the latter including rolling, twisting or drifting. Inspired from the widely adopted point-spread function (PSF) deconvolution 3D PET reconstruction techniques, here we introduce an image-based 3D generalized motion deconvolution method within the standard 3D maximum-likelihood expectation-maximization (ML-EM) reconstruction framework. In particular, we initially integrate a motion blurring kernel, accounting for every tracked motion within a frame, as an additional MLEM modeling component in the image space (integrated 3D-MCIR). Subsequently, we replaced the integrated model component with a nested iterative Richardson-Lucy (RL) image-based deconvolution method to accelerate the MLEM algorithm convergence rate (RL-3D-MCIR). The final method was evaluated with realistic simulations of whole-body dynamic PET data employing the XCAT phantom and real human bulk motion profiles, the latter estimated from volunteer dynamic MRI scans. In addition, metabolic uptake rate Ki parametric images were generated with the standard Patlak method. Our results demonstrate significant improvement in contrast-to-noise ratio (CNR) and noise-bias performance in both dynamic and parametric images. The proposed nested RL-3D-MCIR method is implemented on the Software for Tomographic Image Reconstruction (STIR) open-source platform and is scheduled for public release