Optimal detection of unusual and significant changes in network Origin-Destination (OD) traffic volumes from simple link load measurements is considered in the paper. The ambient traffic, i.e. the OD traffic matrix corresponding to the non-anomalous network state, is unknown and it is considered here as a nuisance parameter because it can mask the anomalies. Since the OD traffic matrix is not recoverable from simple link load measurements, the anomaly detection is an ill-posed decision-making problem. The method proposed in this paper consists of finding a linear parsimonious model of ambient traffic (nuisance parameter) and detecting anomalies by using an invariant detection algorithm based on a separation of the measurement space into disjoint subspaces corresponding to normal and anomalous network traffic. The method's ability to detect anomalies is evaluated in real traffic from Abilene, a United States backbone network. The theoretically expected results are confirmed.