Ultrafast ultrasound has recently emerged as an alternative to traditional focused ultrasound. By virtue of the low number of insonifications it requires, ultrafast ultrasound enables the imaging of the human body at potentially very high frame rates. However, unaccounted for speed-of-sound variations in the insonified medium often result in phase aberrations in the reconstructed images. The diagnosis capability of ultrafast ultrasound is thus ultimately impeded. Therefore, there is a strong need for adaptive beamforming methods that are resilient to speed-of-sound aberrations. Several of such techniques have been proposed recently but they often lack parallelizability or the ability to directly correct both transmit and receive phase aberrations. In this article, we introduce an adaptive beamforming method designed to address these shortcomings. To do so, we compute the windowed Radon transform of several complex radio-frequency images reconstructed using delay-and-sum. Then, we apply to the obtained local sinograms weighted tensor rank-1 decompositions and their results are eventually used to reconstruct a corrected image. We demonstrate using simulated and in-vitro data that our method is able to successfully recover aberration-free images and that it outperforms both coherent compounding and the recently introduced SVD beamformer. Finally, we validate the proposed beamforming technique on in-vivo data, resulting in a significant improvement of image quality compared to the two reference methods.