[robbystk]

You can do deconvolution using ImageJ, but getting a model of the PSF for an arbitrary aperture is the tricky part. https://imagej.net/Deconvolution

[michrassena]

Would it be as simple as imaging a point with the system and using that as the source for the PSF?

[lp251]

more or less; the flatcam paper has a section on the calibration method (finding the psf)

[michrassena]

In this article, they talk about encoded blur.

http://web.media.mit.edu/~raskar/Mask/

About halfway down the page you can see the out-of-focus point source looks identical to the coded aperture.

While not lensless photography, this seems like a good starting point for those interested in these techniques, especially if I can load the PSF into ImageJ.