http://adsabs.harvard.edu/abs/2009MNRAS.395.1733W.
Title:Compressed sensing imaging techniques for radio interferometry
Authors: Wiaux, Y. et al.
Abstract: 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 sparse or compressible 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 specific 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.

As discussed, reconstructing images from noisy observations is typically considered as an ill-posed problem or an inverse problem. Owing to the personal lack of comprehension in image reconstruction of radio interferometry observation based on sample from Fourier space via inverse Fourier transform, I cannot judge how good this new adaption of compressed sensing for radio astronomical imagery is. I think, however, compressed sensing will take over many of traditional image reconstruction tools due to their shortage in forgiving sparsely represented large data/images .

Please, check my old post on compressed sensing for more references to the subject like the Rice university repository in addition to references from Wiaux et al. It’s a new exciting field with countless applications, already enjoying wide popularity from many scientific and engineering fields. My thought is that well developed compressed sensing algorithms might resolve bandwidth issues in satellite observations/communication by transmiting more images within fractional temporal intervals for improved image reconstruction.

Goodness-of-Fit tests have been essential in astronomy to validate the chosen physical model to observed data whereas the limits of these tests have not been taken into consideration carefully when observed data were put into the model for estimating the model parameters. Therefore, I thought this paper would be helpful to have a thought on the different point of views between the astronomers’ practice of goodness-of-fit tests and the statisticians’ constructing tests. (Warning: the paper is abstract and theoretical.)

This paper began with presenting two approaches to constructing test statistics: 1. some measure of distance between the theoretical and empirical distributions like the Cramer-von Mises and the Komogorov-Smirnov statistics and 2. score test statistics, constructed in a way that the tests is asymptotically normal. As the second approach is preferred, the author confined his study to generalize the theory of score tests. The notion of the Neyman type (NT) test was introduced with very minimal assumptions to shape the statistics.

The author discussed the statistical inverse problems or the deconvolution problems of physics, seismology, optics, and imaging where noisy signals and measurements occur. These inverse problems induce the Neyman’s type statistics under appropriate regularity assumptions.

Other type of NT tests in terms of score functions and their consistency was presented in an abstract fashion.