Here is a new and interesting paper making the connection between another indirect measurement technique and compressive sensing. The paper is entitled Compressed sensing imaging techniques for radio interferometry by Yves Wiaux, Laurent Jacques, Gilles Puy, Anna Scaife and Pierre Vandergheynst. The abstract reads:
Radio interferometry probes astrophysical signals through incomplete and noisy Fourier measurements. The theory of compressed sensing demonstrates that such measurements may actually suffice for accurate reconstruction of the signals. We propose new generic imaging techniques based on convex optimization for global minimization problems defined in this context. The versatility of the framework notably allows introduction of prior information on the signals, which offers the possibility of significant improvements of reconstruction relative to the standard local matching pursuit algorithm CLEAN used in radio astronomy. We illustrate the potential of the approach by studying reconstruction performances on simulations of two different kinds of signals observed with very generic interferometric configurations. The first kind is an intensity field of compact astrophysical objects. The second kind is the imprint of cosmic strings in the temperature field of the cosmic microwave background radiation, of particular interest for cosmology.Unlike optical interferometry, the phase information is not lost in radio inteferometry, hence the need for phase retrieval is not warranted. Technological considerations put requirements in the millimeter range as opposed to micrometer range in the optical domain. For those interested in knowing more about the sampling in the Fourier domain performed in astronomy inteferometry, one can take a look at the very nice explanation given by Damien Segransan in Observability and UV coverage where we learn that the rotation of the Earth is a nice help to the astronomy folks.
Also in astronomy, Jean-Luc Starck just released his nice talk presented at the conference in honor of Jean Morlet entitled "Wavelet in Astronomy: From the Isotropic Undecimated WT to Compressed Sensing". I liked the slide updating us on the Compressive Sensing algorithm being currently implemented on the PACS instrument on Herschel due to be launched this Spring.