  Network tomography has been regarded as one of the most promising
methodologies for performance evaluation and diagnosis of the massive and
decentralized Internet. This paper proposes a new estimation approach for
solving a class of inverse problems in network tomography, based on marginal
distributions of a sequence of one-dimensional linear projections of the
observed data. We give a general identifiability result for the proposed method
and study the design issue of these one dimensional projections in terms of
statistical efficiency. We show that for a simple Gaussian tomography model,
there is an optimal set of one-dimensional projections such that the estimator
obtained from these projections is asymptotically as efficient as the maximum
likelihood estimator based on the joint distribution of the observed data. For
practical applications, we carry out simulation studies of the proposed method
for two instances of network tomography. The first is for traffic demand
tomography using a Gaussian Origin-Destination traffic model with a power
relation between its mean and variance, and the second is for network delay
tomography where the link delays are to be estimated from the end-to-end path
delays. We compare estimators obtained from our method and that obtained from
using the joint distribution and other lower dimensional projections, and show
that in both cases, the proposed method yields satisfactory results.
