LOFAR sparse image reconstruction

Abstract

Context. The LOFAR (LOw Frequency ARray) radio telescope is a giant digital phased array interferometer with multiple antennas distributed in Europe. It provides discrete sets of Fourier components of the sky brightness. Recovering the original brightness distribution with aperture synthesis forms an inverse problem that can be solved by various deconvolution and minimization methods. Aims. Recent papers have established a clear link between the discrete nature of radio interferometry measurement and the "compressed sensing" (CS) theory, which supports sparse reconstruction methods to form an image from the measured visibilities. Empowered by proximal theory, CS offers a sound framework for efficient global minimization and sparse data representation using fast algorithms. Combined with instrumental direction-dependent effects (DDE) in the scope of a real instrument, we developed and validated a new method based on this framework. Methods. We implemented a sparse reconstruction method in the standard LOFAR imaging tool and compared the photometric and resolution performance of this new imager with that of CLEAN-based methods (CLEAN and MS-CLEAN) with simulated and real LOFAR data. Results. We show that i) sparse reconstruction performs as well as CLEAN in recovering the flux of point sources, ii) performs much better on extended objects (the root mean square error is reduced by a factor of up to 10), and iii) provides a solution with an effective angular resolution 2-3 times better than the CLEAN images. Conclusions. Sparse recovery gives a correct photometry on high dynamic and wide-field images and improved realistic structures of extended sources (of simulated and real LOFAR datasets). This sparse reconstruction method is compatible with modern interferometric imagers that handle DDE corrections (A-and W-projections) required for current and future instruments such as LOFAR and SKA.

Imaging the Schwarzschild-radius-scale Structure of M87 with the Event Horizon Telescope Using Sparse Modeling

“…Furthermore, previous studies of sparse image reconstruction techniques have shown that regularization with ℓ 1 +wavelet/curvelet transformation is also a promising approach (e.g., Li et al 2011;Carrillo et al 2012Carrillo et al , 2014Garsden et al 2015;Dabbech et al 2015). We will test these sparse regularizations in a forthcoming paper.…”

“…However, it is not straightforward to extend the idea for the problems with multiple regularization functions. For another example, Garsden et al (2015) proposes another heuristic method to determine the regularization parameters on ℓ 1 -regularization on the wavelet/curvelet-transformed image by estimating its noise level on each scale, which is successful. However, the method would not work for all types of regularization functions.…”

“…In the context of compressed sensing (also known as "compressive sensing"), it has been revealed that an ill-posed linear problem may be solved accurately if the underling solution vector is sparse (Candes & Tao 2006;Donoho 2006). Since then, many imaging methods 16 have been applied to radio interferometry after pioneering work by Wiaux et al (2009a) and Wiaux et al (2009b); (see Garsden et al 2015, and references therein). We call these approaches "sparse modeling" since they utilize the sparsity of the ground truth.…”

“…Such a situation may occur for an extended source or also even for a compact source if the imaging pixel size is set to be much smaller than the size of the emission structure. Pioneering work has made use of transforms to wavelet or curvelet basesin which the image can be represented sparsely (e.g., Li et al 2011;Carrillo et al 2012Carrillo et al , 2014Dabbech et al 2015;Garsden et al 2015). As another strategy to resolve this potential issue, in Honma et al (2014), we proposed the addition ofanother regularization, Total Variation (TV; e.g., Rudin et al 1992), which is another popular regularization in sparse modeling.…”

A parallel and automatically tuned algorithm for multispectral image deconvolution

“…A greedy alternative to the minimization of a regularized cost function was proposed by Dabbech et al (2015). Sparse image representations using wavelet dictionaries has indisputably shown substantial improvement with respect to classical CLEAN-based approaches, as demonstrated by Garsden et al (2015) using LOFAR data and Dabbech et al (2018) using VLA data. The price to pay is an increased computational cost and a lot of effort has gone into designing scalable methods able to cope with large data sets.…”