Have you seen light field photography [1]? It would seem that your array is quite similar in concept. I'd imagine that getting images similar to those produced by various SONAR imaging technologies is a similar sort of deconvolution problem. If you're looking for textbooks or scientific papers to review, I think the field of tomography is also ripe with methods to explore here.

I'd challenge the notion however that this isn't 'just' a passive SONAR device. Keeping the camera analogy, active SONAR use spread spectrum pings, much like the white light of a camera's flash. Your camera lacks a flash function, and its lens is maybe not yet as in focus as it could be.

If you did want to add a flash, you're likely a $0.02 piezo device and maybe $20 in other various parts (and heaps of numerical processing on a PC) away from having the ability to produce a nice 3D reconstruction of the physical scene.

If you get direct data capture going, please do post some raw data online. I'm sure others would have heaps of fun playing around with it.

1: http://graphics.stanford.edu/projects/lightfield/

Hm, why not - here is the raw data (after PDM decoding) for the 16x16 video from the article: http://orbides.org/etc/snd_16x16_raw.tar.gz (4 Mb)

One file per cell, 16bit integer samples. Stored row by row, 128 slices per frame.

Not sure where to post it, however - here it would be buried.