Simultaneous Iterative Reconstruction Research Articles

Simultaneous Maximum-Likelihood Reconstruction of Absorption Coefficient, Refractive Index and Dark-Field Scattering Coefficient in X-Ray Talbot-Lau Tomography.

A maximum-likelihood reconstruction technique for X-ray Talbot-Lau tomography is presented. This technique allows the iterative simultaneous reconstruction of discrete distributions of absorption coefficient, refractive index and a dark-field scattering coefficient. This technique avoids prior phase retrieval in the tomographic projection images and thus in principle allows reconstruction from tomographic data with less than three phase steps per projection. A numerical phantom is defined which is used to evaluate convergence of the technique with regard to photon statistics and with regard to the number of projection angles and phase steps used. It is shown that the use of a random phase sampling pattern allows the reconstruction even for the extreme case of only one single phase step per projection. The technique is successfully applied to measured tomographic data of a mouse. In future, this reconstruction technique might also be used to implement enhanced imaging models for X-ray Talbot-Lau tomography. These enhancements might be suited to correct for example beam hardening and dispersion artifacts and improve overall image quality of X-ray Talbot-Lau tomography.

Fast acoustic velocity tomography of focusing operators

A 2D velocity model was estimated by tomographic imaging of overlapping focusing operators that contain one-way traveltimes, from common-focus points to receivers in an aperture along the earth’s surface. The stability and efficiency of convergence and the quality of the resulting models were improved by a sequence of ideas. We used a hybrid parameterization that has an underlying grid, upon which is superimposed a flexible, pseudolayer model. We first solved for the low-wavenumber parts of the model (approximating it as constant-velocity pseudo layers), then we allowed intermediate wavenumbers (allowing the layers to have linear velocity gradients), and finally did unconstrained iterations to add the highest wavenumber details. Layer boundaries were implicitly defined by focus points that align along virtual marker (reflector) horizons. Each focus point sampled an area bounded by the first and last rays in the data aperture at the surface; this reduced the amount of computation and the size of the effective null space of the solution. Model updates were performed simultaneously for the velocities and the local focus point positions in two steps; local estimates were performed independently by amplitude semblance for each focusing operator within its area of dependence, followed by a tomographic weighting of the local estimates into a global solution for each grid point, subject to the constraints of the parameterization used at that iteration. The system of tomographic equations was solved by simultaneous iterative reconstruction, which is equivalent to a least-squares solution, but it does not involve a matrix inversion. The algorithm was successfully applied to synthetic data for a salt dome model using a constant-velocity starting model; after a total of 25 iterations, the velocity error was [Formula: see text] and the final mean focal point position error was [Formula: see text] wavelength.

Three-dimensional reconstruction of flame temperature and emissivity distribution using optical tomographic and two-colour pyrometric techniques

This paper presents an experimental investigation, visualization and validation in the three-dimensional (3D) reconstruction of flame temperature and emissivity distributions by using optical tomographic and two-colour pyrometric techniques. A multi-camera digital imaging system comprising eight optical imaging fibres and two RGB charged-couple device (CCD) cameras are used to acquire two-dimensional (2D) images of the flame simultaneously from eight equiangular directions. A combined logical filtered back-projection (LFBP) and simultaneous iterative reconstruction and algebraic reconstruction technique (SART) algorithm is utilized to reconstruct the grey-level intensity of the flame for the two primary colour (red and green) images. The temperature distribution of the flame is then determined from the ratio of the reconstructed grey-level intensities and the emissivity is estimated from the ratio of the grey level of a primary colour image to that of a blackbody source at the same temperature. The temperature measurement of the system was calibrated using a blackbody furnace as a standard temperature source. Experimental work was undertaken to validate the flame temperature obtained by the imaging system against that obtained using high-precision thermocouples. The difference between the two measurements is found no greater than ±9%. Experimental results obtained on a laboratory-scale propane fired combustion test rig demonstrate that the imaging system and applied technical approach perform well in the reconstruction of the 3D temperature and emissivity distributions of the sooty flame.

Three-dimensional electrostatic potential of a Si p-n junction revealed using tomographic electron holography

Off-axis electron holography and tomography have been combined to examine the 3-D electrostatic potential associated with a thin specimen containing a Si p-n junction. The device was prepared in a novel specimen geometry using focused ion beam milling, and a series of holograms was acquired over a tilt range of -70° to 70°. Simultaneous iterative reconstruction was used to reconstruct the 3-D electrostatic potential in the specimen. The experimental results were compared with simulations of the potential variation. Quantitative results from the central, 'bulk' semiconducting regions and from the surface layers were extracted from the 3-D reconstruction.

Use of High-Performance Computing Algorithms in Combination With Parallel Computing for Tomography

The electron microscope is essential for resolving complex biological structures, such as mitochondria, which are too small to be viewed in detail with the light microscope. In contrast to a conventional instrument, the High-Voltage Electron Microscope (HVEM) located at the National Center for Microscopy and Imaging Research (NCMIR) can obtain images from relatively thick specimens that contain substantial three-dimensional structure. Though a single image acquired with the HVEM represents a projection through the specimen, tomographic methods can be applied to a set of images acquired from different orientations to derive a three-dimensional representation of its biological structure. Tomography requires extensive computation and considerable processing time on conventional workstations in order to reconstruct the typically large HVEM volumes from the tilt series.In order to expedite tomographic processing, we have implemented both the commonly used singleaxis tilt, R-weighted backprojection algorithm and two iterative reconstruction methods, algebraic reconstruction (ART) and simultaneous iterative reconstruction (SIRT) on the massively parallel Intel Paragon at the San Diego Supercompter Center.

Accelerated image reconstruction using ordered subsets of projection data

The authors define ordered subset processing for standard algorithms (such as expectation maximization, EM) for image restoration from projections. Ordered subsets methods group projection data into an ordered sequence of subsets (or blocks). An iteration of ordered subsets EM is defined as a single pass through all the subsets, in each subset using the current estimate to initialize application of EM with that data subset. This approach is similar in concept to block-Kaczmarz methods introduced by Eggermont et al. (1981) for iterative reconstruction. Simultaneous iterative reconstruction (SIRT) and multiplicative algebraic reconstruction (MART) techniques are well known special cases. Ordered subsets EM (OS-EM) provides a restoration imposing a natural positivity condition and with close links to the EM algorithm. OS-EM is applicable in both single photon (SPECT) and positron emission tomography (PET). In simulation studies in SPECT, the OS-EM algorithm provides an order-of-magnitude acceleration over EM, with restoration quality maintained.

The development of cross hole seismic techniques and case studies

This paper outlines the development of a cross hole seismic tomography package by The Broken Hill Proprietary Co. Ltd. (BHP), as a tool for mineral exploration and mine planning. The methodology of cross hole seismic tomography, field procedures, instrumentation, processing software, and field trials are described.Explosives are principally used as the source of seismic energy. A repetitive source, based on rapid hydrogen-oxygen combustion, has also been developed. Signals are detected by geophone-based detector strings, and recorded by a data acquisition system developed by BHP. Tomographic imaging is conducted by the Algebraic Reconstruction, Back Projection and Simultaneous Iterative Reconstruction techniques.Surveys have been conducted in a number of different geological environments, and include: lead-zinc, iron ore and manganese exploration leases and mines to locate mineralisation and overburden interfaces; underground coal mines to locate regions of mining induced stress; and open cut and underground coal mines to locate coal and overburden contacts. The results of these surveys are discussed.

Cross-hole tomography for strongly variable media with applications to scale model data

Abstract A cross-hole ray tomography system is designed for imaging strongly varying velocity distributions; key features are ray bending and the incorporation of multiple raytraces to update the ray paths as the velocity estimates converge. In this context, convergence means that time residuals are stationary both between tomography iterations and between raytraces. For strongly variable velocities, simultaneous iterative reconstruction is recommended rather than classical algebraic reconstruction (convergence is slower but stability is improved). Picking of arrival times must be very sophisticated and involve many arrivals if structural details are to be resolved. Examples include both synthetic and scale model data.