Is Compressive Sensing a zero-th or a first order capability ?

After watching the inspiring video of Ramesh Raskar's Wishlist for Photography. I am wondering the following:

Is Compressive Sensing to be relegated to a first order sensing technique ?

In the presentation mentioned above, Ramesh shows off the BiDi Screen, A Thin, Depth-Sensing LCD for 3D Interaction using Light Fields ( a paper by Matthew Hirsch, Douglas Lanman, Henry Holtzman, Ramesh Raskar) the LCD screen can recognize what happens in front of it. One of the ways they locate the interacting hand with the screen is through the use of a coded aperture and they resort to a MURA configuration. As you know a MURA configuration means that one can invert it with a simple linear transformation. Why do that when you could use a better coding relying on some Toeplitz coded aperture ( as Roummel Marcia and Rebecca Willett do in Compressive Coded Aperture Superresolution Image Reconstruction ( the slides are here)) and obtain superresolution as shown here or 3D there ?

Because it works OK for the task at hand. We all know that coded aperture done with a compressive sensing twist would lead to superresolution and 3D capabilities but:

• the reconstruction would be much slower
• superresolution may not be needed
• there is a fear that a nonlinear reconstruction process would not fail gracefully.
  

I believe Richard Gordon mentioned the near same reasons in his recent paper (Gordon, R. (2010). Stop breast cancer now! Imagining imaging pathways towards search, destroy, cure and watchful waiting of premetastasis breast cancer) about the reason why ART never caught up compared to Filtered Back-Projection Reconstruction, a situation echoed by Xiaochuan Pan, Emil Sidky and Michael Vannier in the provocative title of their paper: Why do commercial CT scanners still employ traditional, filtered back-projection for image reconstruction?.

Maybe this is just true, maybe what we are looking for is simple enough that having an OK measurement is better than the best possible reconstruction with fewer measurements. Then again, if one wants to use the data for other purposes like labeling and so forth, compressive sensing is the only framework that provides some guarantee that you have acquired all the information, not some part of it. Is that zero-th or first order, I am thinking about a round number, and you ?

If you watch the video all the way, Ramesh is looking forward to being able to label everything as well, can one do that with not enough information ?

Credit: Image taken from the BiDi Screen paper by Matthew Hirsch, Douglas Lanman, Henry Holtzman, Ramesh Raskar