Fast tomographic inspection of cylindrical objects

This paper presents a method for improved analysis of objects with an axial symmetry using X-ray Computed Tomography (CT). Cylindrical coordinates about an axis fixed to the object form the most natural base to check certain characteristics of objects that contain such symmetry, as often occurs with industrial parts. The sampling grid corresponds with the object, allowing for down-sampling hence reducing the reconstruction time. This is necessary for in-line applications and fast quality inspection. With algebraic reconstruction it permits the use of a pre-computed initial volume perfectly suited to fit a series of scans where same-type objects can have different positions and orientations, as often encountered in an industrial setting. Weighted back-projection can also be included when some regions are more likely subject to change, to improve stability. Building on a Cartesian grid reconstruction code, the feasibility of reusing the existing ray-tracers is checked against other researches in the same field.Comment: 13 pages, 13 figures. submitted to Journal Of Nondestructive Evaluation (https://www.springer.com/journal/10921

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

A Streaming Multi-GPU Implementation of Image Simulation Algorithms for Scanning Transmission Electron Microscopy

Simulation of atomic resolution image formation in scanning transmission electron microscopy can require significant computation times using traditional methods. A recently developed method, termed plane-wave reciprocal-space interpolated scattering matrix (PRISM), demonstrates potential for significant acceleration of such simulations with negligible loss of accuracy. Here we present a software package called Prismatic for parallelized simulation of image formation in scanning transmission electron microscopy (STEM) using both the PRISM and multislice methods. By distributing the workload between multiple CUDA-enabled GPUs and multicore processors, accelerations as high as 1000x for PRISM and 30x for multislice are achieved relative to traditional multislice implementations using a single 4-GPU machine. We demonstrate a potentially important application of Prismatic, using it to compute images for atomic electron tomography at sufficient speeds to include in the reconstruction pipeline. Prismatic is freely available both as an open-source CUDA/C++ package with a graphical user interface and as a Python package, PyPrismatic

The Application of Tomographic Reconstruction Techniques to Ill-Conditioned Inverse Problems in Atmospheric Science and Biomedical Imaging

A methodology is presented for creating tomographic reconstructions from various projection data, and the relevance of the results to applications in atmospheric science and biomedical imaging is analyzed. The fundamental differences between transform and iterative methods are described and the properties of the imaging configurations are addressed. The presented results are particularly suited for highly ill-conditioned inverse problems in which the imaging data are restricted as a result of poor angular coverage, limited detector arrays, or insufficient access to an imaging region. The class of reconstruction algorithms commonly used in sparse tomography, the algebraic reconstruction techniques, is presented, analyzed, and compared. These algorithms are iterative in nature and their accuracy depends significantly on the initialization of the algorithm, the so-called initial guess. A considerable amount of research was conducted into novel initialization techniques as a means of improving the accuracy. The main body of this paper is comprised of three smaller papers, which describe the application of the presented methods to atmospheric and medical imaging modalities. The first paper details the measurement of mesospheric airglow emissions at two camera sites operated by Utah State University. Reconstructions of vertical airglow emission profiles are presented, including three-dimensional models of the layer formed using a novel fanning technique. The second paper describes the application of the method to the imaging of polar mesospheric clouds (PMCs) by NASA’s Aeronomy of Ice in the Mesosphere (AIM) satellite. The contrasting elements of straight-line and diffusive tomography are also discussed in the context of ill-conditioned imaging problems. A number of developing modalities in medical tomography use near-infrared light, which interacts strongly with biological tissue and results in significant optical scattering. In order to perform tomography on the diffused signal, simulations must be incorporated into the algorithm, which describe the sporadic photon migration. The third paper presents a novel Monte Carlo technique derived from the optical scattering solution for spheroidal particles designed to mimic mitochondria and deformed cell nuclei. Simulated results of optical diffusion are presented. The potential for improving existing imaging modalities through continual development of sparse tomography and optical scattering methods is discussed

Cycloidal CT with CNN-based sinogram completion and in-scan generation of training data

In x-ray computed tomography (CT), the achievable image resolution is typically limited by several pre-fixed characteristics of the x-ray source and detector. Structuring the x-ray beam using a mask with alternating opaque and transmitting septa can overcome this limit. However, the use of a mask imposes an undersampling problem: to obtain complete datasets, significant lateral sample stepping is needed in addition to the sample rotation, resulting in high x-ray doses and long acquisition times. Cycloidal CT, an alternative scanning scheme by which the sample is rotated and translated simultaneously, can provide high aperture-driven resolution without sample stepping, resulting in a lower radiation dose and faster scans. However, cycloidal sinograms are incomplete and must be restored before tomographic images can be computed. In this work, we demonstrate that high-quality images can be reconstructed by applying the recently proposed Mixed Scale Dense (MS-D) convolutional neural network (CNN) to this task. We also propose a novel training approach by which training data are acquired as part of each scan, thus removing the need for large sets of pre-existing reference data, the acquisition of which is often not practicable or possible. We present results for both simulated datasets and real-world data, showing that the combination of cycloidal CT and machine learning-based data recovery can lead to accurate high-resolution images at a limited dose

Fast GPU-Based Approach to Branchless Distance-Driven Projection and Back-Projection in Cone Beam CT

Modern CT image reconstruction algorithms rely on projection and back-projection operations to refine an image estimate in iterative image reconstruction. A widely-used state-of-the-art technique is distance-driven projection and back-projection. While the distance-driven technique yields superior image quality in iterative algorithms, it is a computationally demanding process. This has a detrimental effect on the relevance of the algorithms in clinical settings. A few methods have been proposed for enhancing the distance-driven technique in order to take advantage of modern computer hardware. This study explores a two-dimensional extension of the branchless method, which is a technique that does not compromise image quality. The extension of the branchless method is named “pre-projection integration” because it gets a performance boost by integrating the data before the projection and back-projection operations. It was written with Nvidia’s CUDA framework and carefully designed for massively parallel graphics processing units (GPUs). The performance and the image quality of the pre-projection integration method were analyzed. Both projection and back-projection are significantly faster with pre-projection integration. The image quality was analyzed using cone beam CT image reconstruction algorithms within Jeffrey Fessler’s Image Reconstruction Toolbox. Images produced from regularized, iterative image reconstruction algorithms using the pre-projection integration method show no significant artifacts

High-resolution ab initio three-dimensional X-ray diffraction microscopy

Coherent X-ray diffraction microscopy is a method of imaging non-periodic isolated objects at resolutions only limited, in principle, by the largest scattering angles recorded. We demonstrate X-ray diffraction imaging with high resolution in all three dimensions, as determined by a quantitative analysis of the reconstructed volume images. These images are retrieved from the 3D diffraction data using no a priori knowledge about the shape or composition of the object, which has never before been demonstrated on a non-periodic object. We also construct 2D images of thick objects with infinite depth of focus (without loss of transverse spatial resolution). These methods can be used to image biological and materials science samples at high resolution using X-ray undulator radiation, and establishes the techniques to be used in atomic-resolution ultrafast imaging at X-ray free-electron laser sources.Comment: 22 pages, 11 figures, submitte