  In this paper, we systematically evaluate the performance of adaptive
adjustment of the relaxation parameters of various iterative algorithms for
X-ray CT reconstruction relying on sparsity priors. Sparsity prior has been
found to be an efficient strategy in CT reconstruction where significantly
fewer attenuation measurements are available. Sparsity prior CT reconstruction
relies on iterative algorithms such as the algebraic reconstruction technique
(ART) to produce a crude reconstruction based on which a sparse approximation
is performed. Data driven adjustment of relaxation has been found to ensure
better convergence than traditional relaxation for ART. In this paper, we study
the performance of such data driven relaxation on a (CS) compressed sensing
environment. State-of-the-art algorithms are implemented and their performance
analyzed in regard to conventional and data-driven relaxation. Experiments are
performed both on simulated and real environments. For the simulated case,
experiments are conducted with and without the presence of noise. Correlation
coefficients, root mean square error, structural similarity index and
perceptual dissimilarity metric were used for the quantitative comparisons of
the results. Experiments reveal that data driven relaxation also ensures
overall better quality reconstruction in a CS environment compared to
traditional relaxation. However, when the data are corrupted by noise,
inconsistencies emerge in the convergence unless a threshold is imposed on the
maximum amendments. Data driven relaxation seems a logical choice to more
rapidly reach the solution. In a compressed sensing environment, especially
when the data are corrupted by noise, a threshold to specify the maximum
amendments needs to be specified. Experimentally, we have set the threshold as
20% of the previous value and thus have ensured more consistency in the
convergence.
