Estimation of the properties of early room reflections is an important task in audio signal processing, with applications in beamforming, source separation, room geometry inference, and spatial audio. While methods exist to blindly estimate the direction of arrival and delay of the early reflections, the blind estimation of reflection amplitudes remains an open problem. This work presents a preliminary attempt to blindly estimate reflection amplitudes. An iterative estimator is suggested, based on maximum likelihood and alternating least squares. We discuss some fundamental scaling ambiguities of the problem, and show connections between the proposed method and raking beamformers. A simulation study demonstrates the effectiveness of the proposed method.