Compressed Sensing: What Can Nonlinear Reconstruction Techniques Bring to Coded Aperture in Space and in Nuclear Medicine ?

Last week, at a presentation Jean-Luc Starck mentioned the French-Chinese ECLAIRs mission [1] still on the drawing board (it is actually very advanced as it will launch in 2009) that may benefit from some of the thinking that currently goes in the reconstruction techniques used in Compressed Sensing. As mentioned before here and here, coded aperture masks have been used in the past forty years because there was a linear reconstruction technique available. Compressed Sensing now enlarges this field by providing non-linear reconstruction techniques. And so the question is: How far will the field change because of these new reconstruction techniques ? Let me try to mention the issues that may be aided and the attendant questions that may need trade studies evaluations.

* In the current configuration of ECLAIRs, it seems that the current mask is not optimal with regards to the linear reconstruction paradigm, can the nonlinear reconstruction technique provided better recovery with the same mask or with a different mask that does not rely on the linear results ?


* In Roberto Accorsi's thesis [2], it is painfully obvious that one needs to think of the coded aperture in nuclear systems in a slightly different way than when considering light based instrumentation. This is because radiation goes through everything. Using Olivier Godet's thesis [3] one can see that similar issues pop up in the space based system. In the case of ECLAIRs, some of the weight added to the camera has to do with shielding the camera on the side. On top of this, the mask itself has to be designed so that it removes 95% of the rays passing through it in the 4-50 keV band.


Since, we can model most of the rays going through the camera (Olivier Godet's thesis used Geant and other Monte Carlo codes), is the mask over-designed ? Since radiation is a linear process, could we get more information by delineating some of the signal going through the mask, in other words, can we reduce the 95% mark down to 50% and use the nonlinear reconstruction techniques. This could initially be a mass saving issue but I am sure that this type of activity would do in advancing the state of the art in gamma ray camera for medical purposes on earth.

* Finally, as shown in the presentation of ECLAIRs, the satellite is there to respond to unanticipated bursts. Most data goes through the X-band for transmission, but the VHF band is used to alert the ground that an event is unfolding.


Can the alert system be a simple one based on the smaller number of compressed measurements directly taken by the coded aperture ?


References:
[1] The ECLAIRs micro-satellite for multi-wavelength studies of gamma-ray burst prompt emission
[2] Roberto Accorsi, Design of near-field coded aperture cameras for high resolution medical and industrial gamma-ray imaging. June 2001, MIT.
[3] Olivier Godet, Simulations de la Camera d'imagerie grand champ d'ECLAIRs