  We present a method that takes as input a single dual-pixel image, and
simultaneously estimates the image's defocus map -- the amount of defocus blur
at each pixel -- and recovers an all-in-focus image. Our method is inspired
from recent works that leverage the dual-pixel sensors available in many
consumer cameras to assist with autofocus, and use them for recovery of defocus
maps or all-in-focus images. These prior works have solved the two recovery
problems independently of each other, and often require large labeled datasets
for supervised training. By contrast, we show that it is beneficial to treat
these two closely-connected problems simultaneously. To this end, we set up an
optimization problem that, by carefully modeling the optics of dual-pixel
images, jointly solves both problems. We use data captured with a consumer
smartphone camera to demonstrate that, after a one-time calibration step, our
approach improves upon prior works for both defocus map estimation and blur
removal, despite being entirely unsupervised.
