There have been multiple implementations of this class of algorithm (collectively "synthetic aperture") using different techniques.

Edit: below mentions the HTC "double camera" phones, and in fact it's also possible to create synthetic aperture photography with multiple cameras instead of moving a single camera to multiple positions. Then you have the added advantage of not needing to assume a static scene! But a single-camera algorithm is great for rolling out to the common devices most of us have in our pockets.

Marc Levoy's SynthCam used a circular wiping motion, and attempted to "paint" the 3d space occupied by your theoretical processed aperture.

This Google Camera only requires a single linear move, and processes the rest!