Real-time tomographic reconstruction

With tomography it is possible to reconstruct the interior of an object without destroying. It is an important technique for many applications in, e.g., science, industry, and medicine. The runtime of conventional reconstruction algorithms is typically much longer than the time it takes to perform the tomographic experiment, and this prohibits the real-time reconstruction and visualization of the imaged object. The research in this dissertation introduces various techniques such as new parallelization schemes, data partitioning methods, and a quasi-3D reconstruction framework, that significantly reduce the time it takes to run conventional tomographic reconstruction algorithms without affecting image quality. The resulting methods and software implementations put reconstruction times in the same ballpark as the time it takes to do a tomographic scan, so that we can speak of real-time tomographic reconstruction.NWONumber theory, Algebra and Geometr

A geometric partitioning method for distributed tomographic reconstruction

Tomography is a powerful technique for 3D imaging of the interior of an object. With the growing sizes of typical tomographic data sets, the computational requirements for algorithms in tomography are rapidly increasing. Parallel and distributed-memory methods for tomographic reconstruction are therefore becoming increasingly common. An underexposed aspect is the effect of the data distribution on the performance of distributed-memory reconstruction algorithms. In this work, we introduce a geometric partitioning method, which takes into account the acquisition geometry and aims to minimize the necessary communication between nodes for distributed-memory forward projection and back projection operations. These operations are crucial subroutines for an important class of reconstruction methods. We show that the choice of data distribution has a significant impact on the runtime of these methods. With our novel partitioning method we reduce the communication volume drastically compared to straightforward distributions, by up to 90% for a number of cases, and furthermore we guarantee a specified load balance

Fast Mojette Transform for Discrete Tomography

A new algorithm for reconstructing a two dimensional object from a set of one dimensional projected views is presented that is both computationally exact and experimentally practical. The algorithm has a computational complexity of O(n log2 n) with n = N^2 for an NxN image, is robust in the presence of noise and produces no artefacts in the reconstruction process, as is the case with conventional tomographic methods. The reconstruction process is approximation free because the object is assumed to be discrete and utilizes fully discrete Radon transforms. Noise in the projection data can be suppressed further by introducing redundancy in the reconstruction. The number of projections required for exact reconstruction and the response to noise can be controlled without comprising the digital nature of the algorithm. The digital projections are those of the Mojette Transform, a form of discrete linogram. A simple analytical mapping is developed that compacts these projections exactly into symmetric periodic slices within the Discrete Fourier Transform. A new digital angle set is constructed that allows the periodic slices to completely fill all of the objects Discrete Fourier space. Techniques are proposed to acquire these digital projections experimentally to enable fast and robust two dimensional reconstructions.Comment: 22 pages, 13 figures, Submitted to Elsevier Signal Processin

Joint Image Reconstruction and Segmentation Using the Potts Model

We propose a new algorithmic approach to the non-smooth and non-convex Potts problem (also called piecewise-constant Mumford-Shah problem) for inverse imaging problems. We derive a suitable splitting into specific subproblems that can all be solved efficiently. Our method does not require a priori knowledge on the gray levels nor on the number of segments of the reconstruction. Further, it avoids anisotropic artifacts such as geometric staircasing. We demonstrate the suitability of our method for joint image reconstruction and segmentation. We focus on Radon data, where we in particular consider limited data situations. For instance, our method is able to recover all segments of the Shepp-Logan phantom from $7$ angular views only. We illustrate the practical applicability on a real PET dataset. As further applications, we consider spherical Radon data as well as blurred data

Deterministic Versus Randomized Kaczmarz Iterative Projection

Kaczmarz's alternating projection method has been widely used for solving a consistent (mostly over-determined) linear system of equations Ax=b. Because of its simple iterative nature with light computation, this method was successfully applied in computerized tomography. Since tomography generates a matrix A with highly coherent rows, randomized Kaczmarz algorithm is expected to provide faster convergence as it picks a row for each iteration at random, based on a certain probability distribution. It was recently shown that picking a row at random, proportional with its norm, makes the iteration converge exponentially in expectation with a decay constant that depends on the scaled condition number of A and not the number of equations. Since Kaczmarz's method is a subspace projection method, the convergence rate for simple Kaczmarz algorithm was developed in terms of subspace angles. This paper provides analyses of simple and randomized Kaczmarz algorithms and explain the link between them. It also propose new versions of randomization that may speed up convergence

GPU-Based 3D Cone-Beam CT Image Reconstruction for Large Data Volume

Currently, 3D cone-beam CT image reconstruction speed is still a severe limitation for clinical application. The computational power of modern graphics processing units (GPUs) has been harnessed to provide impressive acceleration of 3D volume image reconstruction. For extra large data volume exceeding the physical graphic memory of GPU, a straightforward compromise is to divide data volume into blocks. Different from the conventional Octree partition method, a new partition scheme is proposed in this paper. This method divides both projection data and reconstructed image volume into subsets according to geometric symmetries in circular cone-beam projection layout, and a fast reconstruction for large data volume can be implemented by packing the subsets of projection data into the RGBA channels of GPU, performing the reconstruction chunk by chunk and combining the individual results in the end. The method is evaluated by reconstructing 3D images from computer-simulation data and real micro-CT data. Our results indicate that the GPU implementation can maintain original precision and speed up the reconstruction process by 110–120 times for circular cone-beam scan, as compared to traditional CPU implementation

Novel high performance techniques for high definition computer aided tomography

Mención Internacional en el título de doctorMedical image processing is an interdisciplinary field in which multiple research areas are involved: image acquisition, scanner design, image reconstruction algorithms, visualization, etc. X-Ray Computed Tomography (CT) is a medical imaging modality based on the attenuation suffered by the X-rays as they pass through the body. Intrinsic differences in attenuation properties of bone, air, and soft tissue result in high-contrast images of anatomical structures. The main objective of CT is to obtain tomographic images from radiographs acquired using X-Ray scanners. The process of building a 3D image or volume from the 2D radiographs is known as reconstruction. One of the latest trends in CT is the reduction of the radiation dose delivered to patients through the decrease of the amount of acquired data. This reduction results in artefacts in the final images if conventional reconstruction methods are used, making it advisable to employ iterative reconstruction algorithms. There are numerous reconstruction algorithms available, from which we can highlight two specific types: traditional algorithms, which are fast but do not enable the obtaining of high quality images in situations of limited data; and iterative algorithms, slower but more reliable when traditional methods do not reach the quality standard requirements. One of the priorities of reconstruction is the obtaining of the final images in near real time, in order to reduce the time spent in diagnosis. To accomplish this objective, new high performance techniques and methods for accelerating these types of algorithms are needed. This thesis addresses the challenges of both traditional and iterative reconstruction algorithms, regarding acceleration and image quality. One common approach for accelerating these algorithms is the usage of shared-memory and heterogeneous architectures. In this thesis, we propose a novel simulation/reconstruction framework, namely FUX-Sim. This framework follows the hypothesis that the development of new flexible X-ray systems can benefit from computer simulations, which may also enable performance to be checked before expensive real systems are implemented. Its modular design abstracts the complexities of programming for accelerated devices to facilitate the development and evaluation of the different configurations and geometries available. In order to obtain near real execution times, low-level optimizations for the main components of the framework are provided for Graphics Processing Unit (GPU) architectures. Other alternative tackled in this thesis is the acceleration of iterative reconstruction algorithms by using distributed memory architectures. We present a novel architecture that unifies the two most important computing paradigms for scientific computing nowadays: High Performance Computing (HPC). The proposed architecture combines Big Data frameworks with the advantages of accelerated computing. The proposed methods presented in this thesis provide more flexible scanner configurations as they offer an accelerated solution. Regarding performance, our approach is as competitive as the solutions found in the literature. Additionally, we demonstrate that our solution scales with the size of the problem, enabling the reconstruction of high resolution images.El procesamiento de imágenes médicas es un campo interdisciplinario en el que participan múltiples áreas de investigación como la adquisición de imágenes, diseño de escáneres, algoritmos de reconstrucción de imágenes, visualización, etc. La tomografía computarizada (TC) de rayos X es una modalidad de imágen médica basada en el cálculo de la atenuación sufrida por los rayos X a medida que pasan por el cuerpo a escanear. Las diferencias intrínsecas en la atenuación de hueso, aire y tejido blando dan como resultado imágenes de alto contraste de estas estructuras anatómicas. El objetivo principal de la TC es obtener imágenes tomográficas a partir estas radiografías obtenidas mediante escáneres de rayos X. El proceso de construir una imagen o volumen en 3D a partir de las radiografías 2D se conoce como reconstrucción. Una de las últimas tendencias en la tomografía computarizada es la reducción de la dosis de radiación administrada a los pacientes a través de la reducción de la cantidad de datos adquiridos. Esta reducción da como resultado artefactos en las imágenes finales si se utilizan métodos de reconstrucción convencionales, por lo que es aconsejable emplear algoritmos de reconstrucción iterativos. Existen numerosos algoritmos de reconstrucción disponibles a partir de los cuales podemos destacar dos categorías: algoritmos tradicionales, rápidos pero no permiten obtener imágenes de alta calidad en situaciones en las que los datos son limitados; y algoritmos iterativos, más lentos pero más estables en situaciones donde los métodos tradicionales no alcanzan los requisitos en cuanto a la calidad de la imagen. Una de las prioridades de la reconstrucción es la obtención de las imágenes finales en tiempo casi real, con el fin de reducir el tiempo de diagnóstico. Para lograr este objetivo, se necesitan nuevas técnicas y métodos de alto rendimiento para acelerar estos algoritmos. Esta tesis aborda los desafíos de los algoritmos de reconstrucción tradicionales e iterativos, con respecto a la aceleración y la calidad de imagen. Un enfoque común para acelerar estos algoritmos es el uso de arquitecturas de memoria compartida y heterogéneas. En esta tesis, proponemos un nuevo sistema de simulación/reconstrucción, llamado FUX-Sim. Este sistema se construye alrededor de la hipótesis de que el desarrollo de nuevos sistemas de rayos X flexibles puede beneficiarse de las simulaciones por computador, en los que también se puede realizar un control del rendimiento de los nuevos sistemas a desarrollar antes de su implementación física. Su diseño modular abstrae las complejidades de la programación para aceleradores con el objetivo de facilitar el desarrollo y la evaluación de las diferentes configuraciones y geometrías disponibles. Para obtener ejecuciones en casi tiempo real, se proporcionan optimizaciones de bajo nivel para los componentes principales del sistema en las arquitecturas GPU. Otra alternativa abordada en esta tesis es la aceleración de los algoritmos de reconstrucción iterativa mediante el uso de arquitecturas de memoria distribuidas. Presentamos una arquitectura novedosa que unifica los dos paradigmas informáticos más importantes en la actualidad: computación de alto rendimiento (HPC) y Big Data. La arquitectura propuesta combina sistemas Big Data con las ventajas de los dispositivos aceleradores. Los métodos propuestos presentados en esta tesis proporcionan configuraciones de escáner más flexibles y ofrecen una solución acelerada. En cuanto al rendimiento, nuestro enfoque es tan competitivo como las soluciones encontradas en la literatura. Además, demostramos que nuestra solución escala con el tamaño del problema, lo que permite la reconstrucción de imágenes de alta resolución.This work has been mainly funded thanks to a FPU fellowship (FPU14/03875) from the Spanish Ministry of Education. It has also been partially supported by other grants: • DPI2016-79075-R. “Nuevos escenarios de tomografía por rayos X”, from the Spanish Ministry of Economy and Competitiveness. • TIN2016-79637-P Towards unification of HPC and Big Data Paradigms from the Spanish Ministry of Economy and Competitiveness. • Short-term scientific missions (STSM) grant from NESUS COST Action IC1305. • TIN2013-41350-P, Scalable Data Management Techniques for High-End Computing Systems from the Spanish Ministry of Economy and Competitiveness. • RTC-2014-3028-1 NECRA Nuevos escenarios clinicos con radiología avanzada from the Spanish Ministry of Economy and Competitiveness.Programa Oficial de Doctorado en Ciencia y Tecnología InformáticaPresidente: José Daniel García Sánchez.- Secretario: Katzlin Olcoz Herrero.- Vocal: Domenico Tali