Knowing what amount of radioactive material was released from Fukushima in March 2011 is crucial to understand the scope of the consequences. Moreover, it could be used in forward simulations to obtain accurate maps of deposition. But these data are often not publicly available, or are of questionable quality. We propose to estimate the emission waveforms by solving an inverse problem. Previous approaches rely on a detailed expert guess of how the releases appeared, and they produce a solution strongly biased by this guess. If we plant a nonexistent peak in the guess, the solution also exhibits a nonexistent peak. We propose a method based on sparse regularization that solves the Fukushima inverse problem blindly. Together with the atmospheric dispersion models and worldwide radioactivity measurements our method correctly reconstructs the times of major events during the accident, and gives plausible estimates of the released quantities of Xenon.