Point-scanning two-photon microscopy enables high-resolution imaging within scattering specimens such as the mammalian brain, but sequential acquisition of voxels fundamentally limits its speed. We developed a two-photon imaging technique that scans lines of excitation across a focal plane at multiple angles and computationally recovers high-resolution images, attaining voxel rates of over 1 billion Hz in structured samples. Using a static image as a prior for recording neural activity, we imaged visually evoked and spontaneous glutamate release across hundreds of dendritic spines in mice at depths over 250 µm and frame rates over 1 kHz. Dendritic glutamate transients in anesthetized mice are synchronized within spatially contiguous domains spanning tens of micrometers at frequencies ranging from 1-100 Hz. We demonstrate millisecond-resolved recordings of acetylcholine and voltage indicators, three-dimensional single-particle tracking and imaging in densely labeled cortex. Our method surpasses limits on the speed of raster-scanned imaging imposed by fluorescence lifetime.