Parameter selection methods for axisymmetric flame tomography through Tikhonov regularization

Deconvolution of optically collected axisymmetric flame data is equivalent to solving an ill-posed problem subject to severe error amplification. Tikhonov regularization has recently been shown to be well suited for stabilizing this deconvolution, although the success of this method hinges on choosing a suitable regularization parameter. Incorporating a parameter selection scheme transforms this technique into a reliable automatic algorithm that outperforms unregularized deconvolution of a smoothed data set, which is currently the most popular way to analyze axisymmetric data. We review the discrepancy principle, L-curve curvature, and generalized cross-validation parameter selection schemes and conclude that the L-curve curvature algorithm is best suited to this problem.