Robust dimensionality reduction for interferometric imaging of Cygnus A

Extremely high data rates expected in next-generation radio interferometers necessitate a fast and robust way to process measurements in a big data context. Dimensionality reduction can alleviate computational load needed to process these data, in terms of both computing speed and memory usage. In this article, we present image reconstruction results from highly reduced radio-interferometric data, following our previously proposed data dimensionality reduction method, Rsing, based on studying the distribution of the singular values of the measurement operator. This method comprises a simple weighted, subsampled discrete Fourier transform of the dirty image. Additionally, we show that an alternative gridding-based reduction method works well for target data sizes of the same order as the image size. We reconstruct images from well-calibrated VLA data to showcase the robustness of our proposed method down to very low data sizes in a 'real data' setting. We show through comparisons with the conventional reduction method of time- and frequency-averaging, that our proposed method produces more accurate reconstructions while reducing data size much further, and is particularly robust when data sizes are aggressively reduced to low fractions of the image size. Rsing can function in a block-wise fashion, and could be used in the future to process incoming data by blocks in real-time, thus opening up the possibility of performing 'on-line' imaging as the data are being acquired. MATLAB code for the proposed dimensionality reduction method is available on GitHub.

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

Dimension embedding for big data in radio interferometry

Rafael Eduardo Carrillo Rangel, Vijay Kartik, Yves Wiaux

As radio telescope data is now increasingly high-dimensional, data reduction has become essential to reduce computational load while preserving accurate signal reconstruction. Gridding the continuous Fourier visibilities represents the standard approach to dimension reduction in radio interferometric imaging. This abstract describes a novel dimension embedding technique relying on the multiplication of the data vector by a fat matrix whose entries are drawn from an i.i.d. random Gaussian distribution. Preliminary results suggest that this approach may provide significant improvement in the reduction of data size with respect to standard gridding, for a given target imaging quality.

2015

A Fourier dimensionality reduction model for big data interferometric imaging

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

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.

Oxford Univ Press2017

A Fourier dimensionality reduction model for big data interferometric imaging

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

Oxford Univ Press2017