Four-dimensional tomographic reconstruction by time domain decomposition

Since the beginnings of tomography, the requirement that the sample does not change during the acquisition of one tomographic rotation is unchanged. We derived and successfully implemented a tomographic reconstruction method which relaxes this decades-old requirement of static samples. In the presented method, dynamic tomographic data sets are decomposed in the temporal domain using basis functions and deploying an L1 regularization technique where the penalty factor is taken for spatial and temporal derivatives. We implemented the iterative algorithm for solving the regularization problem on modern GPU systems to demonstrate its practical use

PyHST2: an hybrid distributed code for high speed tomographic reconstruction with iterative reconstruction and a priori knowledge capabilities

We present the PyHST2 code which is in service at ESRF for phase-contrast and absorption tomography. This code has been engineered to sustain the high data flow typical of the third generation synchrotron facilities (10 terabytes per experiment) by adopting a distributed and pipelined architecture. The code implements, beside a default filtered backprojection reconstruction, iterative reconstruction techniques with a-priori knowledge. These latter are used to improve the reconstruction quality or in order to reduce the required data volume and reach a given quality goal. The implemented a-priori knowledge techniques are based on the total variation penalisation and a new recently found convex functional which is based on overlapping patches. We give details of the different methods and their implementations while the code is distributed under free license. We provide methods for estimating, in the absence of ground-truth data, the optimal parameters values for a-priori techniques

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

Fast algorithms and efficient GPU implementations for the Radon transform and the back-projection operator represented as convolution operators

The Radon transform and its adjoint, the back-projection operator, can both be expressed as convolutions in log-polar coordinates. Hence, fast algorithms for the application of the operators can be constructed by using FFT, if data is resampled at log-polar coordinates. Radon data is typically measured on an equally spaced grid in polar coordinates, and reconstructions are represented (as images) in Cartesian coordinates. Therefore, in addition to FFT, several steps of interpolation have to be conducted in order to apply the Radon transform and the back-projection operator by means of convolutions. Both the interpolation and the FFT operations can be efficiently implemented on Graphical Processor Units (GPUs). For the interpolation, it is possible to make use of the fact that linear interpolation is hard-wired on GPUs, meaning that it has the same computational cost as direct memory access. Cubic order interpolation schemes can be constructed by combining linear interpolation steps which provides important computation speedup. We provide details about how the Radon transform and the back-projection can be implemented efficiently as convolution operators on GPUs. For large data sizes, speedups of about 10 times are obtained in relation to the computational times of other software packages based on GPU implementations of the Radon transform and the back-projection operator. Moreover, speedups of more than a 1000 times are obtained against the CPU-implementations provided in the MATLAB image processing toolbox

Recent advances in x-ray cone-beam computed laminography

X-ray computed tomography is a well established volume imaging technique used routinely in medical diagnosis, industrial non-destructive testing, and a wide range of scientific fields. Traditionally, computed tomography uses scanning geometries with a single axis of rotation together with reconstruction algorithms specifically designed for this setup. Recently there has however been increasing interest in more complex scanning geometries. These include so called X-ray computed laminography systems capable of imaging specimens with large lateral dimensions, or large aspect ratios, neither of which are well suited to conventional CT scanning procedures. Developments throughout this field have thus been rapid, including the introduction of novel system trajectories, the application and refinement of various reconstruction methods, and the use of recently developed computational hardware and software techniques to accelerate reconstruction times. Here we examine the advances made in the last several years and consider their impact on the state of the art

Tomografia estendida : do básico até o mapeamento de cérebro de camundongos

Orientador: Mateus Borba CardosoTese (doutorado) - Universidade Estadual de Campinas, Instituto de Física Gleb WataghinResumo: Esta tese apresentará uma introdução a imagens de raios-x e como adquirir e processar imagens usando linhas de luz síncrotron. Apresentará os desafios matemáticos e técnicos para reconstruir amostras em três dimensões usando a reconstrução de Tomografia Computadorizada, uma técnica conhecida como CT. Esta técnica tem seu campo de visão limitado ao tamanho da câmera e ao tamanho da iluminação. Uma técnica para ampliar esse campo de visão vai ser apresentada e os desafios técnicos envolvidos para que isso aconteça. Um \textit{pipeline} é proposto e todos os algoritmos necessários foram empacotados em um pacote python chamado Tomosaic. A abordagem baseia-se em adquirir tomogramas parciais em posiçoes pré definidas e depois mesclar os dados em um novo conjunto de dados. Duas maneiras possíveis são apresentadas para essa mescla, uma no domínio das projeções e uma no domínio dos sinogramas. Experimentos iniciais serão então usadas para mostrar que o método proposto funciona com computadores normais. A técnica será aplicada mais tarde para pesquisar a anatomia de cérebros de camundongo completos. Um estudo será apresentado de como obter informação em diferentes escalas do cérebro completo do rato utilizando raios-xAbstract: This thesis will present an introduction to x-ray images and how to acquire and thread images using synchrotron beamlines. It will present the mathematical and technical challenges to reconstruct samples in three dimensions using Computed Tomography reconstruction, a technique known as CT. This technique has a field of view bounded to the camera size and the illumination size. A technique to extended this field of view is going to be presented and the technical challenges involved in order for that to happen will be described. A pipeline is proposed and all the necessary algorithms are contained into a python packaged called Tomosaic. The approach relies on acquired partial tomogram data in a defined grid and later merging the data into a new dataset. Two possible ways are presented in order to that: in the projection domain, and in the sinogram domain. Initial experiments will then be used to show that the pipeline works with normal computers. The technique will be later applied to survey the whole anatomy of whole mouse brains. A study will be shown of how to get the complete range of scales of the mouse brain using x-ray tomography at different resolutionsDoutoradoFísicaDoutor em Ciências163304/2013-01247445/2013, 1456912/2014CNPQCAPE

Distributed optimization for nonrigid nano-tomography

Resolution level and reconstruction quality in nano-computed tomography (nano-CT) are in part limited by the stability of microscopes, because the magnitude of mechanical vibrations during scanning becomes comparable to the imaging resolution, and the ability of the samples to resist beam damage during data acquisition. In such cases, there is no incentive in recovering the sample state at different time steps like in time-resolved reconstruction methods, but instead the goal is to retrieve a single reconstruction at the highest possible spatial resolution and without any imaging artifacts. Here we propose a joint solver for imaging samples at the nanoscale with projection alignment, unwarping and regularization. Projection data consistency is regulated by dense optical flow estimated by Farneback's algorithm, leading to sharp sample reconstructions with less artifacts. Synthetic data tests show robustness of the method to Poisson and low-frequency background noise. Applicability of the method is demonstrated on two large-scale nano-imaging experimental data sets.Comment: Manuscript and supplementary materia