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Precise and Automated Tomographic Reconstruction with a Limited Number of Projections

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Precise and Automated Tomographic Reconstruction with a Limited Number of Projections Precise and Automated Tomographic Reconstruction with a Limited Number of Projections Zur Erlangung des akademischen Grades eines DOKTOR-INGENIEURS an der Fakultät für Elektrotechnik und Informationstechnik des Karlsruher Instituts für Technologie (KIT) genehmigte Dissertation von M.Eng. Xiaoli Yang geb. in Shandong Province, China Hauptreferent: Prof. Dr. rer. nat. Marc Weber Korreferent: Prof. Dr. rer. nat. Olaf Dössel Tag der mündlichen Prüfung: 12.01.2016 KIT – University of the State of Baden-Württemberg and National Research Center of the Helmholtz Association www.kit.edu This document is licensed under the Creative Commons Attribution – Share Alike 3.0 DE License (CC BY-SA 3.0 DE): http://creativecommons.org/licenses/by-sa/3.0/de/ Ich versichere wahrheitsgemäß, die Dissertation bis auf die dort angegebene Hilfe selb- ständig angefertigt, alle benutzten Hilfsmittel vollständig und genau angegeben und alles kenntlich gemacht zu haben, was aus Arbeiten anderer und eigenen Veröffentlichungen unverändert oder mit Änderungen entnommen wurde. Karlsruhe, den Xiaoli Yang Abstract X-ray computed tomography (CT) is a popular, non-invasive technique capable of pro- ducing high spatial resolution images. It is generally utilized to provide structural infor- mation of objects to examine. In multiple applications, such as biology, material, and medical science, more and more attention has been paid to tomographic imaging with a limited amount of projections. In this thesis, the tomographic imaging with a limited amount of projections is important in adapting a rapid imaging process or limiting the X- ray radiation exposure to a low level. However, fewer projections normally imply poorer quality of image reconstruction with artifacts by the traditional filtered back-projection (FBP) method, hampering the image analysis and interpretation. A new reconstruction method other than the FBP method is demanded for reducing the projections from over a thousand to around a hundred. Guided by compressive sampling (CS) theory, iterative reconstruction technique based on sparsity helps to overcome these difficulties; however the iterative reconstruction has a number of drawbacks that are tackled in this thesis to allow an automated, fast and high quality reconstruction on a computer cluster. The main component of the framework and contribution of this thesis is a parameter- optimized iterative reconstruction method (optimized-CGTV). It is proposed for tomo- graphic reconstruction with limited projections subject to the minimization of the total variation (TV). This inverse problem is formulated in a Lagrangian multiplier fashion with the parameter optimization by applying a discrete L-curve obtained from the plot of the TV regularization versus data fidelity. The reconstruction is carried out using the corresponding developed conjugate gradient solver to minimize the TV-regularized for- mulation. The optimized-CGTV reconstruction method is incorporated into an automatic framework of parallel 3D reconstruction on a computer cluster to achieve a rapid recon- struction process. The proposed method is evaluated with various datasets, including both simulated and synchrotron X-ray tomographic data (such as the imaging of grain weevil and frog em- bryo). The reconstructions of simulated and experimental data from around 100 pro- jections separately demonstrate the high quality reconstruction by the optimized-CGTV method in both noiseless case and cases subject to different levels of noise. The optimized- CGTV reconstruction reduces strealine artifacts, which appear in the FBP reconstruction due to insufficient projection data, while well preserving main edges of homogeneous structures. With the parallel reconstruction framework in the computer cluster, a 3D vol- ume reconstruction can be completed in the order of 10 minutes with a speedup factor over a hundred compared to the sequential implementation. This reconstruction performance is accepted as near real-time for offline analysis. The method in this thesis has been applied to three tomographic data sources: X-ray tomo- graphic imaging at the TOPO-TOMO bending-magnet beamline of ANKA, X-ray tomo- graphic imaging at the undulator beamline 32-ID of APS, and electron tomographic imag- ing for nanostructured material analysis. In all these applications, the optimized-CGTV method can automatically produce high quality reconstruction from a limited number of projections. As a result, this work enables the building of fast tomography at ANKA, constrains the X-ray radiation dose to extend the scale of in vivo time-lapse series for de- velopmental biology, and allows more precise analysis of nanostructured materials using electron tomography. Zusammenfassung Röntgen-Computertomographie (CT) ist eine etablierte, nichtinvasive Technik zur Erzeu- gung hochauflösender Volumenbilder. Sie wird üblicherweise dazu benutzt, Strukturin- formationen untersuchter Objekte zu gewinnen. In Anwendungsbereichen wie der Biolo- gie, der Medizin und den Materialwissenschaften wird zunehmend Augenmerk auf To- mographie mit wenigen Projektionen gelegt. Diese ist beispielsweise bei schnellen Auf- nahmeverfahren oder speziellen Aufnahmegeometrien von Bedeutung, oder dann, wenn die Strahlungsdosis auf ein geringes Maß reduziert werden soll. Eine geringere Zahl an Projektion bedingt jedoch eine verschlechterte Bildqualität mit Rekonstruktionsarte- fakten, so dass es zu Problemen in der anschließenden Bildanalyse kommt. Dies legt den Bedarf an einer neuen Rekonstruktionsmethode nahe, die nicht den Einschränkun- gen der traditionell verwendeten gefilterten Rückprojektion (Filtered Back-Projection, FBP) unterliegt und Artefaktbildung vermeidet. Unter Zuhilfenahme der Compressive- Sensing-Theorie (CS-Theorie) können iterative Rekonstruktionsmethoden, die sich die Eigenschaft der Dünn-Besetztheit (Sparsity) zunutze machen, solche Rekonstruktion- sprobleme verhindern. Die Anwendung solcher Methoden ist jedoch durch die Parame- terabhängigkeiten, die üblicherweise empirische Parameterbestimmung, den manuellen Implementierungsaufwand und die hohe Rechenzeitanforderungen schwierig. Um dieser Herausforderung zu begegnen, wird in der vorliegenden Arbeit eine parame- teroptimierte iterative Rekonstruktionsmethode für die Computertomographie aufgrund weniger Projektionen vorgestellt. Wichtigstes Optimierungskriterium bei der Rekonstruk- tion eines präzisen 3D-Bildes ist dabei eine Regularisierung der totalen Variation (TV) im Sinne der CS-Theorie. Die iterative Rekonstruktion wird mit Hilfe der Methode der Lagrange-Multiplikatoren formuliert, wobei die Parameteroptimierung in der Anwendung der diskreten L-Kurventheorie besteht, bei der die Datentreue und die TV-Regularisierung gegeneinander abgewogen werden. Diese Rekonstruktionsmethode wird in ein eigens entwickeltes, automatisches Framework eingebettet, das zur schnellen, parallelen 3D- Rekonstruktion in einem Rechencluster dient. Das automatische Framework wird anhand verschiedener Datensätze evaluiert, die sich sowohl aus simulierten als auch aus echten Synchrotron-Röntgentomographiedaten zusam- mensetzen. Für die Echtdaten wurden unter anderem ein Kornkäfer als auch ein Froschem- bryo untersucht. Die Rekonstruktionen der simulierten und der echten Daten mit einer begrenzten Zahl von Projektionen demonstrieren die hohe Bildqualität der entwickel- ten Methode sowohl im rauschfreien als auch im Fall unterschiedlich starken Rauschens. Mit dem entwickelten parallelen Rekonstruktionsframework ist es möglich, 3D-Volumen- rekonstruktionen mit einem hohen Beschleunigungsfakor gegenüber der sequentiellen Implementierung durchzuführen, womit nun Nah-Echtzeit-Rekonstruktionen für Offline- Analyse möglich sind. Die vorgestellte Methode wird für drei verschiedene tomographische Datenquellen einge- setzt: Röntgentomographie der TOPO-TOMO-Beamline (Bending-Magnet-Technik) bei ANKA, Röntgentomographie in der Undulator-Beamline 32-D bei APS und Elektronen- tomographie mit Nanometer-Auflösung. In alle Anwendungen lieferte die entwickelte Methode präzise Rekonstruktionsergebnisse bei eine geringen Anzahl von Projektionen. Die geringe Zahl an Projektionen geht mit geringerer Strahlenbelastung bei gleichbleiben- der Bildqualität einher und ermöglicht beispielsweise in der Entwicklungsbiologie, eine maßgebliche Reduktion der Expositionszeit bei In-Vivo-Messserien. Im Fall der Elektro- nentomographie ist nun eine genauere Analyse nanostrukturierter Materialien möglich. Contents Contents 1. Introduction 1 1.1. Background . .1 1.2. Motivations for sparse-view reconstruction . .6 1.3. State of the art . .9 1.4. Challenges . 13 1.5. Proposed methods . 15 1.6. Main contributions . 17 1.7. Thesis overview . 17 2. Forward problem in computed tomography 19 2.1. X-ray imaging . 19 2.2. Concepts for computed tomographic imaging . 21 2.3. Radon transform . 24 2.4. Fourier-slice theorem . 26 2.5. Digitization and forward models . 27 2.6. Summary . 31 3. Computed tomographic reconstruction 33 3.1. Problem statement . 33 3.2. Analytical reconstruction methods . 35 3.3. Iterative reconstruction methods . 42 3.4. Comparison . 51 3.5. Summary . 55 4. CT reconstruction with limited number of projections 57 4.1. Compressive sampling in CT . 57 4.2. Total variation-based reconstruction . 61 4.3. CGTV solver . 62 4.4. Reconstruction with the CGTV solver . 64 4.5. Summary . 69 5. Optimized CGTV for automated reconstruction 71 5.1. Parameter optimization . 71 5.2. Discrete L-curve method to fix TV regularization . 73 I Contents 5.3. Strategy
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