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

Abstract

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.