  We introduce a novel technique for the reconstruction of multimode optical
fields, based on simultaneously exploiting both the generalized Glauber's
$K^{th}$-order correlation function $g^{(K)}$ and a recently proposed
anti-correlation function (dubbed $\theta^{(K)}$) which is resilient to
Poissonian noise. We experimentally demonstrate that this method yields mode
reconstructions with higher fidelity with respect to those obtained with
reconstruction methods based only on $g^{(K)}$'s, even requiring less "a
priori" information. The reliability and versatility of our technique make it
suitable for a widespread use in real applications of optical quantum
measurement, from quantum information to quantum metrology, especially when one
needs to characterize ensembles of single-photon emitters in the presence of
background noise (due, for example, to residual excitation laser, stray light,
or unwanted fluorescence).
