P. Munshi

A ROBUST MART ALGORITHM FOR TOMOGRAPHIC APPLICATIONS

The present work is concerned with the development of a robust reconstruction algorithm for applications involving tomography. In an earlier study it was shown that among the ART family of algorithms, the multiplicative algebraic reconstruction algorithm (MART) was the most appropriate for tomographic reconstruction [1]. In the present work, the MART algorithm has been extended so that (a) its performance is now acceptable over a wider range of relaxation factors, (b) the time requirement for convergence to a solution is lower, and (c) its performance is less sensitive to noise in the projection data. Applications considered for evaluating the proposed algorithms are (1) a circular region with holes, (2) a three-dimensional temperature field in a differentially heated fluid layer, and (3) experimental data recorded in a differentially heated fluid layer using an interferometer. The proposed algorithms are seen to be an improvement over those presently available, for all three examples considered.

Performance of iterative tomographic algorithms applied to non-destructive evaluation with limited data

Iterative tomographic algorithms have been applied to the reconstruction of a two-dimensional object with internal defects from its projections. Nine distinct algorithms with varying numbers of projections and projection angles have been considered. Each projection of the solid object is interpreted as a path integral of the light-sensitive property of the object in the appropriate direction. The integrals are evaluated numerically and are assumed to represent exact data. Errors in reconstruction are defined as the statistics of difference between original and reconstructed objects and are used to compare one algorithm with respect to another. The algorithms used in this work can be classified broadly into three groups, namely the additive algebraic reconstruction technique (ART), the multiplicative algebraic reconstruction technique (MART) and the maximization reconstruction technique (MRT). Additive ART shows a systematic convergence with respect to the number of projections and the value of the relaxation parameter. MART algorithms produce less error at convergence compared to additive ART but converge only at small values of the relaxation parameter. The MRT algorithm shows an intermediate performance when compared to ART and MART. An increasing noise level in the projection data increases the error in the reconstructed field. The maximum and RMS errors are highest in ART and lowest in MART for given projection data. Increasing noise levels in the projection data decrease the convergence rates. For all algorithms, a 20% noise level is seen as an upper limit, beyond which the reconstructed field is barely recognizable.

Design of an Isotopic CT Scanner for Two Phase Flow Measurements

A feasibility study including parametric analysis, bubbly flow experimentation and preliminary hardware design has been completed for an isotopic CT scanner to interrogate two phase flows. The study results indicate a high speed fan beam scanner is feasible for measuring two phase flows under transient conditions by performing sequential scans. The major tradeoffs of this device compared to medical scanners are spatial resolution (1.15 cm), density resolution (3%), and source type (Cesium-137).

Error estimates for tomographic inversion

The technique of computerized tomography is studied extensively by engineers as well as mathematicians to improve the quality of reconstructed images. Certain error estimates are available for the reconstruction errors occurring in various tomographic algorithms, in particular the convolution backprojection (CBP) method. The authors present an attempt toward developing some error estimates for predicting the inherent error due to the band-limiting assumption incorporated in the CBP methodology. The norms used are local in character compared to the general norms used in previous studies.

Error analysis of tomographic filters. I: Theory

Abstract The technique of computerized tomography is being studied extensively by engineers, physicists and mathematicians to improve the quality of reconstructed images. Certain error estimates are available for the errors occuring in various tomographic algorithms under the assumption that the object cross-section possesses band-limited projection data. It is known, however, that the cross-section function has a finite support, and hence cannot be band-limited. A Sobolev space analysis has already been reported involving certain error estimates for predicting the inherent error in the convolution backprojection algorithm. The present study is an attempt towards developing a simplified two-dimensional Cartesian formula for predicting the comparative performance of the Fourier filters used in the convolution algorithm. This simplified approach involves the Laplacian of the object function and the second-order (Fourier space) derivatives of the filter functions.

Experimental study of Rayleigh?Benard convection at intermediate Rayleigh numbers using interferometric tomography

An experimental study of Rayleigh–Benard convection in an intermediate aspect ratio box that is square in plan is reported. An intermediate range of Rayleigh numbers has been considered in the study. The fluid employed is air. A Mach–Zehnder interferometer is used to collect the line-of-sight projections of the temperature field in the form of interferometric fringes. Images have been recorded after a sufficient time has elapsed for the initial transients to have been eliminated. Interferograms have been collected from four to six view angles. These are used to obtain the three dimensional temperature field inside the cavity by using tomography. An algebraic reconstruction technique has been used for the inversion of the projection data. The convergence of the iterative inversion procedure was unambiguous and asymptotic. The reconstructed temperature field with a subset of the total data was found to be consistent with the remaining unused projections. Results for two Rayleigh numbers, namely 13 900 and 40 200 have been reported. These were found to correspond to two distinct flow regimes. At these Rayleigh numbers, a well-defined steady state was not observed. At the lower Rayleigh number, the fringes away from the wall showed mild unsteadiness. At the higher Rayleigh number, the fringes were found to switch between two patterns. Results for the dominant mode alone have been presented for this problem. At a Rayleigh number of 13 900, three dimensional flow structures, whose influence is equivalent to longitudinal rolls have been observed. At a Rayleigh number of 40 200, cubic cells have been noted in the cavity. The associated flow pattern is inferred to be a plume rising from the heated plate. The local Nusselt number variation is seen to be consistent with the observed flow patterns.

Performance evaluation of fringe thinning algorithms for interferometric tomography

Abstract The present study is concerned with the sensitivity of reconstruction algorithms to fringe thinning operations, in the context of interferometric tomography. Interferograms obtained from a Mach–Zehnder interferometer are considered as the fringe system. The physical problem considered is fluid convection in a rectangular enclosure that is square in plan, heated from below and cooled from the top. The fringes are line-of-sight integrals of the refractive index and hence the temperature field. The fringe patterns are digitized and stored as strings of numbers using a CCD camera along with an image processing system. Three methods of fringe thinning algorithms are considered. The first algorithm is programmable and is based on the search of minimum intensity within the dark bands of the fringe system. The other two algorithms are, respectively, semi-automatic and manual search procedures for location of the midpoints of the dark bands. The thinned fringes contain information about the projection of the temperature field in the direction of the light beam. These data have been used to reconstruct the three-dimensional temperature field in the fluid layer using principles of tomography. The fringe thinning algorithms have been evaluated in terms of effort required, and differences in the reconstructed temperature field as well as the wall heat transfer rate. The automatic search procedure developed in the present work is found to be best suited in terms of these criteria.

Error analysis of tomographic filters II: results

Abstract The convolution backprojection algorithm (CBP) has been studied from the point-of-view of the already published error formula which relates the error in reconstructions, under certain ideal conditions, to the Fourier-space derivatives of the filter functions employed in CBP. The results, for simulated images representing a damaged nuclear reactor fuel assembly and a cross-section of human brain, indicate that the error pattern obtained is in concurrence with the theory. Experimental results for a pixel size of 20 μm are also included.

Performance evaluation of iterative tomographic algorithms applied to reconstruction of a three-dimensional temperature field

Iterative tomographic algorithms have been applied to the reconstruction of a three-dimensional temperature field (from its projections) for Rayleigh-Renard-type natural-convection problems. Nine distinct algorithms with varying numbers of projections and projection angles have been considered. The three-dimensional temperature field is sliced into a set of two-dimensional planes and reconstruction algorithms are applied to each individual plane. Projection of the temperature field is interpreted as a path integral along a line in the appropriate direction. The integrals are evaluated numerically and are assumed to represent exact data. Errors in reconstruction are defined with field data as reference and are used to compare one algorithm with respect to another. The algorithms used in this work can be broadly classified into three groups: additive algebraic reconstruction technique (ART), multiplicative algebraic reconstruction technique (MART), and maximization reconstruction technique (MRT). Additive A...

Analysis of High-Speed CT Scanners for Non-Medical Applications

There are non-medical applications for CT (computerized tomographic) scanner technology which are feasible and potentially important. We have identified several applications related to the general problem of measuring cross-sectional density distributions in two-phase flowing mixtures and have analyzed a general class of CT scanner designs which suit these applications. Specifically, this paper reports the results of an analysis of CT scanners which (1) are appropriate for two-phase fluid density measurements, (2) are based upon stationary detector array scanner designs, (3) incorporate a rotating isotopic fan-beam source, (4) permit continuous scanning of the object, and (5) can achieve 10 millisecond scan times.