In this paper, an alternative formulation of the time-domain beamforming is proposed using the generalized cross-correlation of measured signals. This formulation uses spatial weighting functions adapted to microphone positions and imaging points. The proposed approach is demonstrated for acoustic source localization using a microphone array, both theoretically and experimentally. An increase in accuracy of acoustic imaging results is shown for both narrow and broadband sources, while a factor of reduction up to 20 in the computation time can be achieved, allowing real-time or volumetric source localization over very large grids.