Generalized-Equiangular Geometry CT: Concept and Shift-Invariant FBP Algorithms

With advanced X-ray source and detector technologies being continuously developed, non-traditional CT geometries have been widely explored. Generalized-Equiangular Geometry CT (GEGCT) architecture, in which an X-ray source might be positioned radially far away from the focus of arced detector array that is equiangularly spaced, is of importance in many novel CT systems and designs. GEGCT, unfortunately, has no theoretically exact and shift-invariant analytical image reconstruction algorithm in general. In this study, to obtain fast and accurate reconstruction from GEGCT and to promote its system design and optimization, an in-depth investigation on a group of approximate Filtered BackProjection (FBP) algorithms with a variety of weighting strategies has been conducted. The architecture of GEGCT is first presented and characterized by using a normalized-radial-offset distance (NROD). Next, shift-invariant weighted FBP-type algorithms are derived in a unified framework, with pre-filtering, filtering, and post-filtering weights. Three viable weighting strategies are then presented including a classic one developed by Besson in the literature and two new ones generated from a curvature fitting and from an empirical formula, where all of the three weights can be expressed as certain functions of NROD. After that, an analysis of reconstruction accuracy is conducted with a wide range of NROD. We further stretch the weighted FBP-type algorithms to GEGCT with dynamic NROD. Finally, the weighted FBP algorithm for GEGCT is extended to a three-dimensional form in the case of cone-beam scan with a cylindrical detector array.Comment: 31 pages, 13 figure

A standard and linear fan-beam Fourier backprojection theorem

We propose a theoretical formulation for the tomographic fan-beam backprojection in standard and linear geometries. The proposed formula is obtained from a recent backprojection formulation for the parallel case. Such formula is written as a Bessel-Neumann series representation in the frequency domain of the target space in polar coordinates. A mathematical proof is provided together with numerical simulations compared with conventional fan-beam backprojection representations to validate our formulation

An FPGA-based 3D backprojector

Subject of this thesis is the hardware architecture for the X-ray Computer Tomography. The main aim of the work is the development of a scalable, high-performance hardware for the reconstruction of a volume from cone-beam projections. A modified Feldkamp cone-beam reconstruction algorithm (Cylindrical algorithm) was used. The modifications of the original algorithm: parallelization and pipelining of the reconstruction, were formalized. Special attention was paid to the architecture of the memory system and to the schedule of the memory accesses.The developed architecture contains all steps of the reconstruction from cone-beam projections: filtering of the detector data, weighted backprojection and on-line geometry computations. The architecture was evaluated for the Xilinx Field Programmable Gate Array (FPGA). The simulations showed that the speed-up of the reconstruction of a volume is about an order of a magnitude compared to the currently available PC implementations.Gegenstand dieser Dissertation ist die Hardware-Architektur für die Röntgen-Computertomographie. Das Hauptziel der Arbeit ist die Entwicklung einer skalierbaren, leistungsstarken Hardware für die Rekonstruktion des Objektvolumens bei der Kegelstrahlprojektion. Dazu wurde ein modifizierter Feldkamp-Kegelstrahl-Rekonstruktionsalgorithmus benutzt (Zylinder-Algorithmus). Die Abwandlungen des Original-Algorithmus, Parallelisierung und Pipelining der Rekonstruktion, werden formal beschrieben. Besonderes Augenmerk wurde auf die Architektur des Speichersystems und das Timing des Speicherzugriffes gelegt. Die entwickelte Architektur enthält alle Schritte der Rekonstruktion von Kegelstrahlprojektionen: die Filterung der Detektordaten, die gewichtete Rückprojektion und Echtzeit-Geometrieberechnungen. Die Architektur wurde für ein Field Programmable Gate Array (FPGA) der Firma Xilinx evaluiert. Die Simulationen zeigten, dass die zur Rekonstruktion des Objektvolumens benötigte Zeit im Vergleich zu konventionellen PC-Implementierungen um eine Größenordnung verkürzt wurde

SparseBeads data: benchmarking sparsity-regularized computed tomography

Sparsity regularization (SR) such as total variation (TV) minimization allows accurate image reconstruction in x-ray computed tomography (CT) from fewer projections than analytical methods. Exactly how few projections suffice and how this number may depend on the image remain poorly understood. Compressive sensing connects the critical number of projections to the image sparsity, but does not cover CT, however empirical results suggest a similar connection. The present work establishes for real CT data a connection between gradient sparsity and the sufficient number of projections for accurate TV-regularized reconstruction. A collection of 48 x-ray CT datasets called SparseBeads was designed for benchmarking SR reconstruction algorithms. Beadpacks comprising glass beads of five different sizes as well as mixtures were scanned in a micro-CT scanner to provide structured datasets with variable image sparsity levels, number of projections and noise levels to allow the systematic assessment of parameters affecting performance of SR reconstruction algorithms6. Using the SparseBeads data, TV-regularized reconstruction quality was assessed as a function of numbers of projections and gradient sparsity. The critical number of projections for satisfactory TV-regularized reconstruction increased almost linearly with the gradient sparsity. This establishes a quantitative guideline from which one may predict how few projections to acquire based on expected sample sparsity level as an aid in planning of dose- or time-critical experiments. The results are expected to hold for samples of similar characteristics, i.e. consisting of few, distinct phases with relatively simple structure. Such cases are plentiful in porous media, composite materials, foams, as well as non-destructive testing and metrology. For samples of other characteristics the proposed methodology may be used to investigate similar relations

An FPGA-based 3D backprojector

Subject of this thesis is the hardware architecture for the X-ray Computer Tomography. The main aim of the work is the development of a scalable, high-performance hardware for the reconstruction of a volume from cone-beam projections. A modified Feldkamp cone-beam reconstruction algorithm (Cylindrical algorithm) was used. The modifications of the original algorithm: parallelization and pipelining of the reconstruction, were formalized. Special attention was paid to the architecture of the memory system and to the schedule of the memory accesses.The developed architecture contains all steps of the reconstruction from cone-beam projections: filtering of the detector data, weighted backprojection and on-line geometry computations. The architecture was evaluated for the Xilinx Field Programmable Gate Array (FPGA). The simulations showed that the speed-up of the reconstruction of a volume is about an order of a magnitude compared to the currently available PC implementations.Gegenstand dieser Dissertation ist die Hardware-Architektur für die Röntgen-Computertomographie. Das Hauptziel der Arbeit ist die Entwicklung einer skalierbaren, leistungsstarken Hardware für die Rekonstruktion des Objektvolumens bei der Kegelstrahlprojektion. Dazu wurde ein modifizierter Feldkamp-Kegelstrahl-Rekonstruktionsalgorithmus benutzt (Zylinder-Algorithmus). Die Abwandlungen des Original-Algorithmus, Parallelisierung und Pipelining der Rekonstruktion, werden formal beschrieben. Besonderes Augenmerk wurde auf die Architektur des Speichersystems und das Timing des Speicherzugriffes gelegt. Die entwickelte Architektur enthält alle Schritte der Rekonstruktion von Kegelstrahlprojektionen: die Filterung der Detektordaten, die gewichtete Rückprojektion und Echtzeit-Geometrieberechnungen. Die Architektur wurde für ein Field Programmable Gate Array (FPGA) der Firma Xilinx evaluiert. Die Simulationen zeigten, dass die zur Rekonstruktion des Objektvolumens benötigte Zeit im Vergleich zu konventionellen PC-Implementierungen um eine Größenordnung verkürzt wurde

Artefact Reduction Methods for Iterative Reconstruction in Full-fan Cone Beam CT Radiotherapy Applications

A cone beam CT (CBCT) system acquires two-dimensional projection images of an imaging object from multiple angles in one single rotation and reconstructs the object geometry in three dimensions for volumetric visualization. It is mounted on most modern linear accelerators and is routinely used in radiotherapy to verify patient positioning, monitor patient contour changes throughout the course of treatment, and enable adaptive radiotherapy planning. Iterative image reconstruction algorithms use mathematical methods to iteratively solve the reconstruction problem. Iterative algorithms have demonstrated improvement in image quality and / or reduction in imaging dose over traditional filtered back-projection (FBP) methods. However, despite the advancement in computer technology and growing availability of open-source iterative algorithms, clinical implementation of iterative CBCT has been limited. This thesis does not report development of codes for new iterative image reconstruction algorithms. It focuses on bridging the gap between the algorithm and its implementation by addressing artefacts that are the results of imperfections from the raw projections and from the imaging geometry. Such artefacts can severely degrade image quality and cannot be removed by iterative algorithms alone. Practical solutions to solving these artefacts will be presented and this in turn will better enable clinical implementation of iterative CBCT reconstruction

Compressed Sensing Based Reconstruction Algorithm for X-ray Dose Reduction in Synchrotron Source Micro Computed Tomography

Synchrotron computed tomography requires a large number of angular projections to reconstruct tomographic images with high resolution for detailed and accurate diagnosis. However, this exposes the specimen to a large amount of x-ray radiation. Furthermore, this increases scan time and, consequently, the likelihood of involuntary specimen movements. One approach for decreasing the total scan time and radiation dose is to reduce the number of projection views needed to reconstruct the images. However, the aliasing artifacts appearing in the image due to the reduced number of projection data, visibly degrade the image quality. According to the compressed sensing theory, a signal can be accurately reconstructed from highly undersampled data by solving an optimization problem, provided that the signal can be sparsely represented in a predefined transform domain. Therefore, this thesis is mainly concerned with designing compressed sensing-based reconstruction algorithms to suppress aliasing artifacts while preserving spatial resolution in the resulting reconstructed image. First, the reduced-view synchrotron computed tomography reconstruction is formulated as a total variation regularized compressed sensing problem. The Douglas-Rachford Splitting and the randomized Kaczmarz methods are utilized to solve the optimization problem of the compressed sensing formulation. In contrast with the first part, where consistent simulated projection data are generated for image reconstruction, the reduced-view inconsistent real ex-vivo synchrotron absorption contrast micro computed tomography bone data are used in the second part. A gradient regularized compressed sensing problem is formulated, and the Douglas-Rachford Splitting and the preconditioned conjugate gradient methods are utilized to solve the optimization problem of the compressed sensing formulation. The wavelet image denoising algorithm is used as the post-processing algorithm to attenuate the unwanted staircase artifact generated by the reconstruction algorithm. Finally, a noisy and highly reduced-view inconsistent real in-vivo synchrotron phase-contrast computed tomography bone data are used for image reconstruction. A combination of prior image constrained compressed sensing framework, and the wavelet regularization is formulated, and the Douglas-Rachford Splitting and the preconditioned conjugate gradient methods are utilized to solve the optimization problem of the compressed sensing formulation. The prior image constrained compressed sensing framework takes advantage of the prior image to promote the sparsity of the target image. It may lead to an unwanted staircase artifact when applied to noisy and texture images, so the wavelet regularization is used to attenuate the unwanted staircase artifact generated by the prior image constrained compressed sensing reconstruction algorithm. The visual and quantitative performance assessments with the reduced-view simulated and real computed tomography data from canine prostate tissue, rat forelimb, and femoral cortical bone samples, show that the proposed algorithms have fewer artifacts and reconstruction errors than other conventional reconstruction algorithms at the same x-ray dose