In this paper, a novel multi-target sparse localization (SL) algorithm based on compressive sampling (CS) is proposed. Different from the existing literature for target counting and localization where signal/received-signal-strength (RSS) readings at different access points (APs) are used separately, we propose to reformulate the SL problem so that we can make use of the cross-correlations of the signal readings at different APs. We analytically show that this new framework can provide a considerable amount of extra information compared to classical SL algorithms. We further highlight that in some cases this extra information converts the under-determined problem of SL into an over-determined problem for which we can use ordinary least-squares (LS) to efficiently recover the target vector even if it is not sparse. Our simulation results illustrate that compared to classical SL this extra information leads to a considerable improvement in terms of number of localizable targets as well as localization accuracy.