  Video reconstruction from a single motion-blurred image is a challenging
problem, which can enhance the capabilities of existing cameras. Recently,
several works addressed this task using conventional imaging and deep learning.
Yet, such purely-digital methods are inherently limited, due to direction
ambiguity and noise sensitivity. Some works proposed to address these
limitations using non-conventional image sensors, however, such sensors are
extremely rare and expensive. To circumvent these limitations with simpler
means, we propose a hybrid optical-digital method for video reconstruction that
requires only simple modifications to existing optical systems. We use a
learned dynamic phase-coding in the lens aperture during the image acquisition
to encode the motion trajectories, which serve as prior information for the
video reconstruction process. The proposed computational camera generates a
sharp frame burst of the scene at various frame rates from a single coded
motion-blurred image, using an image-to-video convolutional neural network. We
present advantages and improved performance compared to existing methods, using
both simulations and a real-world camera prototype. We extend our optical
coding also to video frame interpolation and present robust and improved
results for noisy videos.
