We propose a new strategy for narrow band, active array imaging of weak localized scatterers when only the intensities are recorded and measured at the array. We consider a homogeneous medium so that wave propagation is fully coherent. We show that imaging with intensity-only measurements can be carried out using the time reversal operator of the imaging system, which can be obtained from intensity measurements using an appropriate illumination strategy and the polarization identity. Once the time reversal operator has been obtained, we show that the images can be formed using its singular value decomposition (SVD). We use two SVD-based methods to image the scatterers. The proposed approach is simple and efficient. It does not need prior information about the sought image, and it guarantees exact recovery in the noise-free case. Furthermore, it is robust with respect to additive noise. Detailed numerical simulations illustrate the performance of the proposed imaging strategy when only the intensities are captured.