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Four-dimensional ultrasound imaging of complex biological systems such as the brain is technically challenging because of the spatiotemporal sampling requirements. We present computational ultrasound imaging (cUSi), a new imaging method that uses complex ultrasound fields that can be generated with simple hardware and a physical wave prediction model to alleviate the sampling constraints. cUSi allows for high-resolution four-dimensional imaging of brain haemodynamics in awake and anesthetized mice.