We present an adaptation of the pixel-reassignment technique from confocal fluorescent microscopy to coherent ultrasound imaging. The method, Ultrasound Pixel-Reassignment (UPR), provides a resolution and signal to noise (SNR) improvement in ultrasound imaging by computationally reassigning off-focus signals acquired using traditional plane-wave compounding ultrasonography. We theoretically analyze the analogy between the optical and ultrasound implementations of pixel reassignment, and experimentally evaluate the imaging quality on tissue-mimicking acoustic phantoms. We demonstrate that UPR provides a $25\%$ resolution improvement and a $3dB$ SNR improvement in in-vitro scans, without any change in hardware or acquisition scheme.