A Fourier dimensionality reduction model for big data interferometric imaging

Abstract

Data dimensionality reduction in radio interferometry can provide savings of computational resources for image reconstruction through reduced memory footprints and lighter computations per iteration, which is important for the scalability of imaging methods to the big data setting of the next-generation telescopes. This article sheds new light on dimensionality reduction from the perspective of the compressed sensing theory and studies its interplay with imaging algorithms designed in the context of convex optimization. We propose a post-gridding linear data embedding to the space spanned by the left singular vectors of the measurement operator, providing a dimensionality reduction below image size. This embedding preserves the null space of the measurement operator and hence its sampling properties are also preserved in light of the compressed sensing theory. We show that this can be approximated by first computing the dirty image and then applying a weighted subsampled discrete Fourier transform to obtain the final reduced data vector. This Fourier dimensionality reduction model ensures a fast implementation of the full measurement operator, essential for any iterative image reconstruction method. The proposed reduction also preserves the i.i.d. Gaussian properties of the original measurement noise. For convex optimization-based imaging algorithms, this is key to justify the use of the standard 2 -norm as the data fidelity term. Our simulations confirm that this dimensionality reduction approach can be leveraged by convex optimization algorithms with no loss in imaging quality relative to reconstructing the image from the complete visibility data set. Reconstruction results in simulation settings with no direction dependent effects or calibration errors show promising performance of the proposed dimensionality reduction. Further tests on real data are planned as an extension of the current work. matlab code implementing the proposed reduction method is available on GitHub.

An optimized algorithm for multiscale wideband deconvolution of radio astronomical images

“…Nevertheless, due to its instability when real data is used, the MORESANE and IUWT convex optimization algorithms are only useful in very specific cases. So far, most compressed sensing methods for radio interferometric deconvolution have only been demonstrated on relatively simple test cases, that do not include calibration errors or w-terms, and with a small number of visibilities and a small image size (e.g., Carrillo et al 2014, Junklewitz et al 2016, Kartik et al 2017. As was shown in this paper, the MORESANE compressed sensing approach does well in simple cases, but performs less well on data with calibration errors or with artefacts from spectral curvature.…”