Tomographic reconstruction using heuristic Monte Carlo methods

A tomographic reconstruction method based on Monte Carlo random searching guided by the information contained in the projections of radiographed objects is presented. In order to solve the optimization problem, a multiscale algorithm is proposed to reduce computation. The reconstruction is performed in a coarse-to-fine multigrid scale that initializes each resolution level with the reconstruction of the previous coarser level, which substantially improves the performance. The method was applied to a real case reconstructing the internal structure of a small metallic object with internal components, showing excellent results.     

Local algorithms in exterior tomography

Exterior tomographic data are taken over lines outside a central region, and such data occur in the industrial nondestructive evaluation of large objects such as rockets. We explain, using microlocal analysis, which singularities are well reconstructed from exterior data, and we explain how this phenomenon is reflected in the singular value decomposition for the exterior transform [E.T. Quinto, Singular value decompositions and inversion methods for the exterior Radon transform and a spherical transform, J. Math. Anal. Appl. 95 (1983) 437–448]. We extend Lambda Tomography to exterior data and to limited angle exterior data. The algorithm is tested on industrial data from Perceptics, Inc.     

Use of x-ray microtomography to visualise dynamic adsorption of organic vapour and water vapour on activated carbon

X-ray microtomography coupled with image analysis was used to quantify the adsorption of vapours on activated carbon beds. This technique was tested using three different challenges: CCl₄, water vapour and a mixture of water- and organic vapour. It is shown that the used technique allows determining the adsorption front progress in the case of organic vapour and mixture of water and organic vapour whereas the existence of this front was not so obvious in the case of water vapour. Experimental results obtained for organic vapours were interpreted on the basis of the Wheeler-Jonas equation: a good agreement was found between experimental and theoretical breakthrough times.     

CT重构中射线硬化的校正研究

在工业CT(ComputedTomography)重构中,由于射束硬化使得重建图像中出现"杯状"伪影。为了消除这种影响,提出了一种校正方法。该方法基于Beer理论,根据多色射束和数据,首先拟合出等效单色射束和数据,然后进行卷积反投影重构。这种方法不仅较好地消除了射线硬化的影响,同时也使重构图像的信息损失不大。     

ICT并行重建算法设计与实现

分析了三维ICT近似重建FDK快速算法以及算法串行执行与并行执行的复杂度,利用MPI并行编程环境,对原有ICT重建流程进行并行化,在PC集群上实现了并行ICT重建,进行了系统集成。给出了系统应用实现的解决方案与软件集成流程图。实验结果证明串行重建和并行重建结果是一致的,并行重建可以得到比较理想地重建时间结果和比较理想的加速比与效率。     

正电子放射层析成象系统设计的计算机模拟

在一个简单实用的数学模型基础上,利用现代计算机技术对正电子放射层析成象系统(PET)进行了模拟,并详细讨论了闪烁晶体材料的物理、几何特性以及探测器环直径的大小对于PET系统的空间分辨率的影响.本文所得的结论对于开发和设计PET系统来说,是非常有用的.     

一种测量多相流流型的ECT图像重建算法

提出了一种新的电容层析成像图像重建算法-IMNSNOF算法.该算法在分析极小范数解的基础之上针对ECT逆问题的特点对其进行改进,并利用奇异值分解定理证明这种改进的数值稳定作用.在此基础上建立新的日标泛函,并在求解该泛函的过程中采用正则技巧对其进行改进确保数值解的稳定性.利用非闭合电极ECT传感器实测了多相流沿流向的流型...     

On the determination of a function from an elliptical Radon transform

In recent years, Radon-type transforms that integrate functions over various sets of ellipses/ellipsoids have been considered in synthetic aperture radar, ultrasound reflection tomography, and radio tomography. In this paper, we consider the transform that integrates a given function in Rⁿ${\mathbb{R}}^n$ over a set of solid ellipses (when n=2$n=2$) or solid ellipsoids of rotation (when n?3$n?3$) with a fixed eccentricity and foci restricted to a hyperplane. Inversion formulas are obtained for appropriate classes of functions that are even with respect to the hyperplane. Stability estimates and local uniqueness results are also provided.     

Tomographic reconstruction of shock layer flows

The tomographic reconstruction of supersonic flows faces two challenges. Firstly, techniques used in the past, such as the direct Fourier method (DFM) (Gottlieb and Gustafsson in On the direct Fourier method for computer tomography, 1998; Morton in Tomographic imaging of supersonic flows, 1995) or various backprojection (Kak and Slaney in Principles of computerized tomographic imaging, vol. 33 in Classics in Applied Mathematics, 2001) techniques, have only been able to reconstruct areas of the flow which are upstream of any opaque objects, such as a model. Secondly, shock waves create sharp discontinuities in flow properties, which can be difficult to reconstruct both in position and in magnitude with limited data. This paper will present a reconstruction method, matrix inversion using ray-tracing and least squares conjugate gradient (MI-RLS), which uses geometric ray-tracing and a sparse matrix iterative solver (Paige and Saunders in ACM Trans. Math. Softw. 8(1):43–71, 1982) to overcome both of these challenges. It will be shown, through testing with a phantom object described in tomographic literature, that the results compare favourably to those produced by the DFM technique. Finally, the method will be used to reconstruct three-dimensional density fields from interferometric shock layer images, with good resolution (Faletič in Tomographic reconstruction of shock layer flows, 2005). This paper was based on work that was presented at the 3rd International Symposium on Interdisciplinary Shock Wave Research, Canberra, Australia, March 1–3, 2006.