Compressed sensing theory is slowly making its way to solve more and more astronomical inverse problems. We address here the application of sparse representations, convex optimization and proximal theory to radio interferometric imaging. First, we ex
pose the theory behind interferometric imaging, sparse representations and convex optimization, and second, we illustrate their application with numerical tests with SASIR, an implementation of the FISTA, a Forward-Backward splitting algorithm hosted in a LOFAR imager. Various tests have been conducted in Garsden et al., 2015. The main results are: i) an improved angular resolution (super resolution of a factor ~2) with point sources as compared to CLEAN on the same data, ii) correct photometry measurements on a field of point sources at high dynamic range and iii) the imaging of extended sources with improved fidelity. SASIR provides better reconstructions (five time less residuals) of the extended emission as compared to CLEAN. With the advent of large radiotelescopes, there is scope for improving classical imaging methods with convex optimization methods combined with sparse representations.
We show the potential for classifying images of mixtures of aggregate, based themselves on varying, albeit well-defined, sizes and shapes, in order to provide a far more effective approach compared to the classification of individual sizes and shapes
. While a dominant (additive, stationary) Gaussian noise component in image data will ensure that wavelet coefficients are of Gaussian distribution, long tailed distributions (symptomatic, for example, of extreme values) may well hold in practice for wavelet coefficients. Energy (2nd order moment) has often been used for image characterization for image content-based retrieval, and higher order moments may be important also, not least for capturing long tailed distributional behavior. In this work, we assess 2nd, 3rd and 4th order moments of multiresolution transform -- wavelet and curvelet transform -- coefficients as features. As analysis methodology, taking account of image types, multiresolution transforms, and moments of coefficients in the scales or bands, we use correspondence analysis as well as k-nearest neighbors supervised classification.
