Mathematics and Algorithms in Tomography

This was the ninth Oberwolfach conference on the mathematics of tomography. Modalities represented at the workshop included X-ray tomography, radar, seismic imaging, ultrasound, electron microscopy, impedance imaging, photoacoustic tomography, elastography, emission tomography, X-ray CT, and vector tomography along with a wide range of mathematical analysis

A Fast and Continuous CT scanner for the optimization of logs in a sawmill

CT Log is a CT scanner used in an industrial process at very high speed in order to optimize the production of wood boards and other wood products. The scanner can reach 160 m/min, the typical speed at which wood logs are sawn in the sawmills. After the logs pass though the scanner, the images are reconstructed and processed in order to allow the automatic optimization of the cutting pattern according to the constraints set by wood defects and the value of the different products. Building a a buffer between the scanner and the sawing line is expensive and often not possible because of constraints on the plant layout The time available for the entire processing is therefore very short, because it must be completed before the log reaches the breakdown equipment. In this paper, we present the structure of the scanner and the way we implemented the different stages of processing in order maximize the speed of the elaboration

Geometrical Calibration and Filter Optimization for Cone-Beam Computed Tomography

This thesis will discuss the requirements of a software library for tomography and will derive a framework which can be used to realize various applications in cone-beam computed tomography (CBCT). The presented framework is self-contained and is realized using the MATLAB environment in combination with native low-level technologies (C/C++ and CUDA) to improve its computational performance, while providing accessibility and extendability through to use of a scripting language environment. On top of this framework, the realization of Katsevich’s algorithm on multicore hardware will be explained and the resulting implementation will be compared to the Feldkamp, Davis and Kress (FDK) algorithm. It will also be shown that this helical reconstruction method has the potential to reduce the measurement uncertainty. However, misalignment artifacts appear more severe in the helical reconstructions from real data than in the circular ones. Especially for helical CBCT (H-CBCT), this fact suggests that a precise calibration of the computed tomography (CT) system is inevitable. As a consequence, a self-calibration method will be designed that is able to estimate the misalignment parameters from the cone-beam projection data without the need of any additional measurements. The presented method employs a multi-resolution 2D-3D registration technique and a novel volume update scheme in combination with a stochastic reprojection strategy to achieve a reasonable runtime performance. The presented results will show that this method reaches sub-voxel accuracy and can compete with current state-of-the-art online- and offline-calibration approaches. Additionally, for the construction of filters in the area of limited-angle tomography a general scheme which uses the Approximate Inverse (AI) to compute an optimized set of 2D angle-dependent projection filters will be derived. Optimal sets of filters are then precomputed for two angular range setups and will be reused to perform various evaluations on multiple datasets with a filtered backprojection (FBP)-type method. This approach will be compared to the standard FDK algorithm and to the simultaneous iterative reconstruction technique (SIRT). The results of the study show that the introduced filter optimization produces results comparable to those of SIRT with respect to the reduction of reconstruction artifacts, whereby its runtime is comparable to that of the FDK algorithm

Efficient Cone Beam Reconstruction For The Distorted Circle And Line Trajectory

We propose an exact filtered backprojection algorithm for inversion of the cone beam data in the case when the trajectory is composed of a distorted circle and a line segment. The length of the scan is determined by the region of interest , and it is independent of the size of the object. With few geometric restrictions on the curve, we show that we have an exact reconstruction. Numerical experiments demonstrate good image quality

Multi-GPU Acceleration of Iterative X-ray CT Image Reconstruction

X-ray computed tomography is a widely used medical imaging modality for screening and diagnosing diseases and for image-guided radiation therapy treatment planning. Statistical iterative reconstruction (SIR) algorithms have the potential to significantly reduce image artifacts by minimizing a cost function that models the physics and statistics of the data acquisition process in X-ray CT. SIR algorithms have superior performance compared to traditional analytical reconstructions for a wide range of applications including nonstandard geometries arising from irregular sampling, limited angular range, missing data, and low-dose CT. The main hurdle for the widespread adoption of SIR algorithms in multislice X-ray CT reconstruction problems is their slow convergence rate and associated computational time. We seek to design and develop fast parallel SIR algorithms for clinical X-ray CT scanners. Each of the following approaches is implemented on real clinical helical CT data acquired from a Siemens Sensation 16 scanner and compared to the straightforward implementation of the Alternating Minimization (AM) algorithm of O’Sullivan and Benac [1]. We parallelize the computationally expensive projection and backprojection operations by exploiting the massively parallel hardware architecture of 3 NVIDIA TITAN X Graphical Processing Unit (GPU) devices with CUDA programming tools and achieve an average speedup of 72X over a straightforward CPU implementation. We implement a multi-GPU based voxel-driven multislice analytical reconstruction algorithm called Feldkamp-Davis-Kress (FDK) [2] and achieve an average overall speedup of 1382X over the baseline CPU implementation by using 3 TITAN X GPUs. Moreover, we propose a novel adaptive surrogate-function based optimization scheme for the AM algorithm, resulting in more aggressive update steps in every iteration. On average, we double the convergence rate of our baseline AM algorithm and also improve image quality by using the adaptive surrogate function. We extend the multi-GPU and adaptive surrogate-function based acceleration techniques to dual-energy reconstruction problems as well. Furthermore, we design and develop a GPU-based deep Convolutional Neural Network (CNN) to denoise simulated low-dose X-ray CT images. Our experiments show significant improvements in the image quality with our proposed deep CNN-based algorithm against some widely used denoising techniques including Block Matching 3-D (BM3D) and Weighted Nuclear Norm Minimization (WNNM). Overall, we have developed novel fast, parallel, computationally efficient methods to perform multislice statistical reconstruction and image-based denoising on clinically-sized datasets

Analysis of Cone-Beam Artifacts in off-Centered Circular CT for Four Reconstruction Methods

Cone-beam (CB) acquisition is increasingly used for truly three-dimensional X-ray computerized tomography (CT). However, tomographic reconstruction from data collected along a circular trajectory with the popular Feldkamp algorithm is known to produce the so-called CB artifacts. These artifacts result from the incompleteness of the source trajectory and the resulting missing data in the Radon space increasing with the distance to the plane containing the source orbit. In the context of the development of integrated PET/CT microscanners, we introduced a novel off-centered circular CT cone-beam geometry. We proposed a generalized Feldkamp formula (α-FDK) adapted to this geometry, but reconstructions suffer from increased CB artifacts. In this paper, we evaluate and compare four different reconstruction methods for correcting CB artifacts in off-centered geometry. We consider the α-FDK algorithm, the shift-variant FBP method derived from the T-FDK, an FBP method based on the Grangeat formula, and an iterative algebraic method (SART). The results show that the low contrast artifacts can be efficiently corrected by the shift-variant method and the SART method to achieve good quality images at the expense of increased computation time, but the geometrical deformations are still not compensated for by these techniques

Methods for Cryo-EM Single Particle Reconstruction of Macromolecules having Continuous Heterogeneity

Macromolecules change their shape (conformation) in the process of carrying out their functions. The imaging by cryo-electron microscopy of rapidly-frozen, individual copies of macromolecules (single particles) is a powerful and general approach to understanding the motions and energy landscapes of macromolecules. Widely-used computational methods already allow the recovery of a few distinct conformations from heterogeneous single-particle samples, but the treatment of complex forms of heterogeneity such as the continuum of possible transitory states and flexible regions remains largely an open problem. In recent years there has been a surge of new approaches for treating the more general problem of continuous heterogeneity. This paper surveys the current state of the art in this area.Comment: 20 pages, 2 figure

Validação de heterogeneidade estrutural em dados de Crio-ME por comitês de agrupadores

Orientadores: Fernando José Von Zuben, Rodrigo Villares PortugalDissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de ComputaçãoResumo: Análise de Partículas Isoladas é uma técnica que permite o estudo da estrutura tridimensional de proteínas e outros complexos macromoleculares de interesse biológico. Seus dados primários consistem em imagens de microscopia eletrônica de transmissão de múltiplas cópias da molécula em orientações aleatórias. Tais imagens são bastante ruidosas devido à baixa dose de elétrons utilizada. Reconstruções 3D podem ser obtidas combinando-se muitas imagens de partículas em orientações similares e estimando seus ângulos relativos. Entretanto, estados conformacionais heterogêneos frequentemente coexistem na amostra, porque os complexos moleculares podem ser flexíveis e também interagir com outras partículas. Heterogeneidade representa um desafio na reconstrução de modelos 3D confiáveis e degrada a resolução dos mesmos. Entre os algoritmos mais populares usados para classificação estrutural estão o agrupamento por k-médias, agrupamento hierárquico, mapas autoorganizáveis e estimadores de máxima verossimilhança. Tais abordagens estão geralmente entrelaçadas à reconstrução dos modelos 3D. No entanto, trabalhos recentes indicam ser possível inferir informações a respeito da estrutura das moléculas diretamente do conjunto de projeções 2D. Dentre estas descobertas, está a relação entre a variabilidade estrutural e manifolds em um espaço de atributos multidimensional. Esta dissertação investiga se um comitê de algoritmos de não-supervisionados é capaz de separar tais "manifolds conformacionais". Métodos de "consenso" tendem a fornecer classificação mais precisa e podem alcançar performance satisfatória em uma ampla gama de conjuntos de dados, se comparados a algoritmos individuais. Nós investigamos o comportamento de seis algoritmos de agrupamento, tanto individualmente quanto combinados em comitês, para a tarefa de classificação de heterogeneidade conformacional. A abordagem proposta foi testada em conjuntos sintéticos e reais contendo misturas de imagens de projeção da proteína Mm-cpn nos estados "aberto" e "fechado". Demonstra-se que comitês de agrupadores podem fornecer informações úteis na validação de particionamentos estruturais independetemente de algoritmos de reconstrução 3DAbstract: Single Particle Analysis is a technique that allows the study of the three-dimensional structure of proteins and other macromolecular assemblies of biological interest. Its primary data consists of transmission electron microscopy images from multiple copies of the molecule in random orientations. Such images are very noisy due to the low electron dose employed. Reconstruction of the macromolecule can be obtained by averaging many images of particles in similar orientations and estimating their relative angles. However, heterogeneous conformational states often co-exist in the sample, because the molecular complexes can be flexible and may also interact with other particles. Heterogeneity poses a challenge to the reconstruction of reliable 3D models and degrades their resolution. Among the most popular algorithms used for structural classification are k-means clustering, hierarchical clustering, self-organizing maps and maximum-likelihood estimators. Such approaches are usually interlaced with the reconstructions of the 3D models. Nevertheless, recent works indicate that it is possible to infer information about the structure of the molecules directly from the dataset of 2D projections. Among these findings is the relationship between structural variability and manifolds in a multidimensional feature space. This dissertation investigates whether an ensemble of unsupervised classification algorithms is able to separate these "conformational manifolds". Ensemble or "consensus" methods tend to provide more accurate classification and may achieve satisfactory performance across a wide range of datasets, when compared with individual algorithms. We investigate the behavior of six clustering algorithms both individually and combined in ensembles for the task of structural heterogeneity classification. The approach was tested on synthetic and real datasets containing a mixture of images from the Mm-cpn chaperonin in the "open" and "closed" states. It is shown that cluster ensembles can provide useful information in validating the structural partitionings independently of 3D reconstruction methodsMestradoEngenharia de ComputaçãoMestre em Engenharia Elétric