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Magnetic resonance imaging and X-ray computed tomography provide the two principal methods available for imaging the brain at high spatial resolution, but these methods are not easily portable and cannot be applied safely to all patients. Ultrasound imaging is portable and universally safe, but existing modalities cannot image usefully inside the adult human skull. We use in silico simulations to demonstrate that full-waveform inversion, a computational technique originally developed in geophysics, is able to generate accurate three-dimensional images of the brain with sub-millimetre resolution. This approach overcomes the familiar problems of conventional ultrasound neuroimaging by using the following: transcranial ultrasound that is not obscured by strong reflections from the skull, low frequencies that are readily transmitted with good signal-to-noise ratio, an accurate wave equation that properly accounts for …