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
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.