Closure

The MART family of algorithms available in the literature was seen to require a small relaxation factor leading to delayed convergence. To address this issue, a new set of algorithms have been proposed in the present work. The new set is conceptually similar to the original, but differs significantly in the manner in which corrections are applied. Specifically, the reconstructed field does not satisfy the projection data, pointwise. However, it can accommodate a wider range of relaxation factors and thus is better from a theoretical view point. Results with the relaxation factor set at unity have been reported in the present work.
The proposed algorithms have been evaluated in the context of three applications, namely: (1)circular disk with five holes, (2) three-dimensional convective thermal field, and (3) interferometric data from a laboratory-scale differentially heated fluid layer experiment. The major results that emerge from the study are:

1. All six algorithms reconstruct the field variable in a qualitative sense. Differences are seen only in the numerical values.
2. The AVMART2 algorithm emerges as the best, in terms of CPU time, errors and sensitivity to initial guess and  noise in the projection data.
3. The CPU time of the proposed algorithms is significantly; smaller than those presently available in the literature.
4. With a limited number of projections, all algorithms show large absolute maximum error, but these are sharply localize. Specifically, the qualitative appearance of the reconstructed field variable is acceptable from a practical viewpoint.
5. The convergence rate of the proposed algorithms is found to be better than the original, when the projection data is exact. In the presence of noise, all the six algo-algorithms  record a sharp reduction in the convergence rate. In a few cases, the proposed algorithms require a greater number of iterations compared to the original. However, in all applications, the CPU time requirement is substantially smaller for the proposed algorithms.