Compressed sensing imaging techniques for radio interferometry

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.Comment: 10 pages, 1 figure. Version 2 matches version accepted for publication in MNRAS. Changes includes: writing corrections, clarifications of arguments, figure update, and a new subsection 4.1 commenting on the exact compliance of radio interferometric measurements with compressed sensin

A regularized tri-linear approach for optical interferometric imaging

“…More generally, for the sparse representation of continuous extended structures, Ψ can be considered as wavelet basis (Mallat 2009), a possibly redundant or a concatenation of non-redundant wavelet basis (Carrillo et al 2012). In this context, the theory of compressive sensing has proven its worth in numerous cases to obtain a unique solution from a highly under-determined problem, relying on the sparsity of the underlying signal (Wiaux et al 2009;Duarte & Eldar 2011). This drives us to use the regularization function g in (7) to promote sparsity in our minimization problem.…”

“…More precisely, in the monochromatic case, we propose to improve the method based on the trilinear data model proposed by Auria et al (2014). First, we propose to impose sparsity as a regularization term, by means of an ℓ 1 -norm, either in the image domain or in a given basis (Wiaux et al 2009;Carrillo et al 2012), leveraging the recent compressive sensing theory (Donoho 2006). In addition, we have developed an algorithm, based on the block-coordinate forward-backward algorithm recently proposed, e.g., by Bolte et al (2014);Frankel et al (2015); Chouzenoux et al (2016), which allows to deal with nonnecessarily smooth regularization terms such as the ℓ 1 norm.…”

“…Classical reconstruction methods for radio interferometry are mainly based on iterative deconvolution (CLEAN; Högbom (1974)), and on maximum entropy methods (MEM) to impose smoothness on the sought image by maximizing the entropy of the image (Cornwell & Evans 1985). More recently, imaging techniques within the framework of compressive sensing have been proposed (Wiaux et al 2009). These methods rely on finding an image that is sparse in a given dictionary, using convex optimization algorithms (Boyd & Vandenberghe 2004;Combettes & Pesquet 2010).…”

Radio Continuum Surveys with Square Kilometre Array Pathfinders

“…Theoretical CS results therefore do not usually improve estimates of astrophysical sources from interferometric data. However, a key ingredient of the CS framework, sparse representations (Mallat 2008), has demonstrated significant improvements in radioastronomical deconvolution, and has been used as a tool for deconvolution of extended and diffuse sources in the image plane (Wiaux et al 2009a;Li et al 2011a;Dabbech, Mary, & Ferrari 2012) as well as in Faraday depth (Li et al 2011b).…”

“…Suksmono 2009;Wiaux et al 2009aWiaux et al , 2009bVannier et al 2010;Wenger et al 2010;McEwen & Wiaux 2011)), including successful simulations of SKA pathfinder observations. Li et al (2011a) present a classical synthesis approach with an IUWT (Isotropic Undecimated Wavelet Transform) synthesis dictionary, Carillo, McEwen, & Wiaux (2012) used an analysis approach using a concatenation of wavelet bases, and Dabbech et al (2012) defined a hybrid analysis-by-synthesis approach.…”