A Fourier dimensionality reduction model for big data interferometric imaging

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 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 also its sampling properties as per 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 L2-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. MATLAB code implementing the proposed reduction method is available on GitHub.

Low-dimensional data embedding for scalable astronomical imaging in the SKA telescope era

Vijay Kartik

Astronomy is one of the oldest sciences known to humanity. We have been studying celestial objects for millennia, and continue to peer deeper into space in our thirst for knowledge about our origins and the universe that surrounds us. Radio astronomy -- observing celestial objects at radio frequencies -- has helped push the boundaries on the kind of objects we can study. Indeed, some of the most important discoveries about the structure of our universe, like the cosmic microwave background, and entire classes of objects like quasars and pulsars, were made using radio astronomy. Radio interferometers are telescopes made of multiple antennas spread over a distance. Signals detected at different antennas are combined to provide images with much higher resolution and sensitivity than with a traditional single-dish radio telescope. The Square Kilometre Array (SKA) is one such radio interferometer, with plans to have antennas separated by as much as 3000,km. In its quest for ever-higher resolution and ever-wider coverage of the sky, the SKA heralds a data explosion, with an expected acquisition rate of 5,terabits per second. The high data rate fed into the pipeline can be handled with a two-pronged approach -- (i) scalable, parallel imaging algorithms that fully utilize the latest computing technologies like accelerators and distributed clusters, and (ii) dimensionality reduction methods that embed the high-dimensional telescope data to much smaller sizes without losing information and guaranteeing accurate recovery of the images, thereby enabling imaging methods to scale to big data sizes and alleviating heavy loads on pipeline buffers without compromising on the science goals of the SKA. In this thesis we propose fast and robust dimensionality reduction methods that embed data to very low sizes while preserving information present in the original data. These methods are presented in the context of compressed sensing theory and related signal recovery techniques. The effectiveness of the reduction methods is illustrated by coupling them with advanced convex optimization algorithms to solve a sparse recovery problem. Images thus reconstructed from extremely low-sized embedded data are shown to have quality comparable to those obtained from full data without any reduction. Comparisons with other standard `data compression' techniques in radio interferometry (like averaging) show a clear advantage in using our methods which provide higher quality images from much lower data sizes. We confirm these claims on both synthetic data simulating SKA data patterns as well as actual telescope data from a state-of-the-art radio interferometer. Additionally, imaging with reduced data is shown to have a lighter computational load -- smaller memory footprint owing to the size and faster iterative image recovery owing to the fast embedding. Extensions to the work presented in this thesis are already underway. We propose an `on-line' version of our reduction methods that works on blocks of data and thus can be applied on-the-fly on data as they are being acquired by telescopes in real-time. This is of immediate interest to the SKA where large buffers in the data acquisition pipeline are very expensive and thus undesirable. Some directions to be probed in the immediate future are in transient imaging, and imaging hyperspectral data to test computational load while in a high resolution, multi-frequency setting.

EPFL2018

Fourier dimensionality reduction of radio-interferometric data

Rafael Eduardo Carrillo Rangel, Vijay Kartik, Jean-Philippe Thiran, Yves Wiaux

Next-generation radio-interferometers face a computing challenge with respect to the imaging techniques that can be applied in the big data setting in which they are designed. Dimensionality reduction can thus provide essential savings of computing resources, allowing imaging methods to scale with data. The work presented here approaches dimensionality reduction from a compressed sensing theory perspective, and links to its role in convex optimization-based imaging algorithms. We describe a novel linear dimensionality reduction technique consisting of a linear embedding to the space spanned by the left singular vectors of the measurement operator. A subsequent approximation of this embedding is shown to be practically implemented through a weighted subsampled Fourier transform of the dirty image. Preliminary results on simulated data with realistic coverages suggest that this approach provides significant reduction of data dimension to well below image size, while achieving comparable image quality to that obtained from the complete data set.

2017

Sparsity Averaging Reweighted Analysis (SARA): a novel algorithm for radio-interferometric imaging

Rafael Eduardo Carrillo Rangel, Jason Douglas McEwen, Yves Wiaux

We propose a novel algorithm for image reconstruction in radio interferometry. The ill-posed inverse problem associated with the incomplete Fourier sampling identified by the visibility measurements is regularized by the assumption of average signal sparsity over representations in multiple wavelet bases. The algorithm, defined in the versatile framework of convex optimization, is dubbed Sparsity Averaging Reweighted Analysis (SARA). We show through simulations that the proposed approach outperforms state-of-the-art imaging methods in the field, which are based on the assumption of signal sparsity in a single basis only.

Wiley-Blackwell2012

Low-dimensional data embedding for scalable astronomical imaging in the SKA telescope era

Vijay Kartik

EPFL2018