  Imaging point sources with low angular separation near or below the Rayleigh
criterion is important in astronomy, e.g., in the search for habitable
exoplanets near stars. However, the measurement time required to resolve stars
in the sub-Rayleigh region via traditional direct imaging is usually
prohibitive. Here we propose quantum-accelerated imaging (QAI) to significantly
reduce the measurement time using an information-theoretic approach. QAI
achieves quantum acceleration by adaptively learning optimal measurements from
data to maximize Fisher information per detected photon. Our approach can be
implemented experimentally by linear-projection instruments followed by a
single-photon detector array. We estimate the position, brightness and the
number of unknown stars $10\sim100$ times faster than direct imaging with the
same aperture. QAI is scalable to large number of incoherent point sources and
can find widespread applicability beyond astronomy to high-speed imaging,
fluorescence microscopy and efficient optical read-out of qubits.
