Well, it's reconstructed just as easily as it's taken. The taking lenses become the viewing lenses.... it works off a phenomenon called the "sampling effect". It's pretty easy to understand, but very hard to explain. Have a look at wikipedia... http://en.wikipedia.org/wiki/Integral_photography
The only catch is that the 1st generation image will be pseudoscopic, that is, a face would look like the inside of a mask. You have to make 2 generations to get an ortho-stereoscopic image. Hence, its limited success as an imaging technique. However, I think a pseudoscopic image would still be worth the effort.
Looking forward to any translations, I'd be more than happy to spruce them up if necessary.