PERFORMANCE EVALUATION OF ITERATIVE TOMOGRAPHIC ALGORITHMS APPLIED TO RECONSTRUCTION OF A THREE-DIMENSIONAL TEMPERATURE FIELD

Abstract

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 ART shows a systematic convergence with respect to number of the projections and the value of the relaxation parameter. MART algorithms produce less error at convergence compared to additive ARTs but converge only at low values of relaxation parameter. In the present work the MRT algorithm shows intermediate performance when compared to ART and MART. Increasing noise level in projection data increases the error in the reconstructed fidd. The maximum and root-mean-square errors are highest in ART and lowest in MART for a given projection data. Increasing noise levels in 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 recognisable.