Reply to comment by Z. S. Yao, R. G. Roberts and A. Tryggvason on ‘Explicit, approximate expressions for the resolution and<i>a posteriori</i>covariance of massive tomographic systems’

Abstract

In their comment, Yao et al. (2001) questioned the accuracy of the algorithm proposed by Nolet et al. (1999) for the approximate estimation of the resolution and covariance matrix of massive tomographic systems. For brevity, we shall refer to the comment and our paper as YRT and NMV, respectively. In NMV we already stressed the approximate nature of the estimation for systems for which an exact computation is infeasible, and we have no difficulty with the viewpoint that further iterations would be desirable if possible—in fact we suggested a straightforward Newtonian scheme in the discussion section of NMV, but did point out that the sparsity of the large matrix will be lost quickly, making iterative schemes prohibitively expensive for large systems. We think that most tomographers would be very happy with one-step resolution estimates such as that shown by YRT in their Figs 6(c) and (d) when compared with the exact results of Figs 6(a) and (b), but leave the ultimate judgement to the reader. In the remaining part of this reply we would like to point out several inaccuracies in YRT that should not remain unanswered.