Ashwin Wagadarikar mentions a page dedicated to his work on hyperspectral imaging using coded/dispersive apertures and using compressed sensing reconstruction techniques to recover data. It adds to a previous entry on the explosive birth of coded aperture on designs using either a single or dual disperser. The paper on the single disperser is now available on that page or you can directly request a preprint from Ashwin. It is an excellent read and as mentioned before, they used the Gradient Projection for Sparse Reconstruction (GPSR) method to perform the reconstructions.
Marco Duarte answers by a comment in a previous entry on their multiscale random projection
where I mentioned that there was no description of the regularizing kernels:
"..For our paper on multiscale random projections, our regularization kernel relies on coarse pixelation, since we were applying our technique on the single pixel camera. This is to say that the random measurements are obtained at different resolutions to get the projections of the different regularizations of the target image..."The ability to command the pixel on the DMD allows for some interesting convolutions. In other words, in order to deal with the non-differentiability of Image Appearance Manifolds, the CS camera has to do smoothing projections at different scales. This process is not unlike the parallel I had made on the current state of the art in compressed sensing and its potential use in the modeling of the primary visual cortex. The thesis of Thomas Serre makes it clear that random projections seem to be in the play (at least in his model that takes into account most of what we know about biological processes). He also shows that those projections are done at different scales as well.