Fundamental Imaging Limits of Radio Telescope Arrays

The fidelity of radio astronomical images is generally assessed by practical experience, i.e. using rules of thumb, although some aspects and cases have been treated rigorously. In this paper we present a mathematical framework capable of describing the fundamental limits of radio astronomical imaging problems. Although the data model assumes a single snapshot observation, i.e. variations in time and frequency are not considered, this framework is sufficiently general to allow extension to synthesis observations. Using tools from statistical signal processing and linear algebra, we discuss the tractability of the imaging and deconvolution problem, the redistribution of noise in the map by the imaging and deconvolution process, the covariance of the image values due to propagation of calibration errors and thermal noise and the upper limit on the number of sources tractable by self calibration. The combination of covariance of the image values and the number of tractable sources determines the effective noise floor achievable in the imaging process. The effective noise provides a better figure of merit than dynamic range since it includes the spatial variations of the noise. Our results provide handles for improving the imaging performance by design of the array.Comment: 12 pages, 8 figure

Multisource Self-calibration for Sensor Arrays

Calibration of a sensor array is more involved if the antennas have direction dependent gains and multiple calibrator sources are simultaneously present. We study this case for a sensor array with arbitrary geometry but identical elements, i.e. elements with the same direction dependent gain pattern. A weighted alternating least squares (WALS) algorithm is derived that iteratively solves for the direction independent complex gains of the array elements, their noise powers and their gains in the direction of the calibrator sources. An extension of the problem is the case where the apparent calibrator source locations are unknown, e.g., due to refractive propagation paths. For this case, the WALS method is supplemented with weighted subspace fitting (WSF) direction finding techniques. Using Monte Carlo simulations we demonstrate that both methods are asymptotically statistically efficient and converge within two iterations even in cases of low SNR.Comment: 11 pages, 8 figure

Fast gain calibration in radio astronomy using alternating direction implicit methods: Analysis and applications

Context. Modern radio astronomical arrays have (or will have) more than one order of magnitude more receivers than classical synthesis arrays, such as the VLA and the WSRT. This makes gain calibration a computationally demanding task. Several alternating direction implicit (ADI) approaches have therefore been proposed that reduce numerical complexity for this task from $\mathcal{O}(P^3)$ to $\mathcal{O}(P^2)$, where $P$ is the number of receive paths to be calibrated. Aims. We present an ADI method, show that it converges to the optimal solution, and assess its numerical, computational and statistical performance. We also discuss its suitability for application in self-calibration and report on its successful application in LOFAR standard pipelines. Methods. Convergence is proved by rigorous mathematical analysis using a contraction mapping. Its numerical, algorithmic, and statistical performance, as well as its suitability for application in self-calibration, are assessed using simulations. Results. Our simulations confirm the $\mathcal{O}(P^2)$ complexity and excellent numerical and computational properties of the algorithm. They also confirm that the algorithm performs at or close to the Cramer-Rao bound (CRB, lower bound on the variance of estimated parameters). We find that the algorithm is suitable for application in self-calibration and discuss how it can be included. We demonstrate an order-of-magnitude speed improvement in calibration over traditional methods on actual LOFAR data. Conclusions. In this paper, we demonstrate that ADI methods are a valid and computationally more efficient alternative to traditional gain calibration method and we report on its successful application in a number of actual data reduction pipelines.Comment: accepted for publication in Astronomy & Astrophysic

Redundancy Calibration of Phased Array Stations

Our aim is to assess the benefits and limitations of using the redundant visibility information in regular phased array systems for improving the calibration. Regular arrays offer the possibility to use redundant visibility information to constrain the calibration of the array independent of a sky model and a beam models of the station elements. It requires a regular arrangement in the configuration of array elements and identical beam patterns. We revised a calibration method for phased array stations using the redundant visibility information in the system and applied it successfully to a LOFAR station. The performance and limitations of the method were demonstrated by comparing its use on real and simulated data. The main limitation is the mutual coupling between the station elements, which leads to non-identical beams and stronger baseline dependent noise. Comparing the variance of the estimated complex gains with the Cramer-Rao Bound (CRB) indicates that redundancy is a stable and optimum method for calibrating the complex gains of the system. Our study shows that the use of the redundant visibility does improve the quality of the calibration in phased array systems. In addition it provides a powerful tool for system diagnostics. Our results demonstrate that designing redundancy in both the station layout and the array configuration of future aperture arrays is strongly recommended. In particular in the case of the Square Kilometre Array with its dynamic range requirement which surpasses any existing array by an order of magnitude.Comment: 16 pages, 15 figures, accepted for publication in the A&A in Section 13, acceptance date: 1st May 2012. NOTE: Please contact the first author for high resolution figure

Calibration Challenges for Future Radio Telescopes

Instruments for radio astronomical observations have come a long way. While the first telescopes were based on very large dishes and 2-antenna interferometers, current instruments consist of dozens of steerable dishes, whereas future instruments will be even larger distributed sensor arrays with a hierarchy of phased array elements. For such arrays to provide meaningful output (images), accurate calibration is of critical importance. Calibration must solve for the unknown antenna gains and phases, as well as the unknown atmospheric and ionospheric disturbances. Future telescopes will have a large number of elements and a large field of view. In this case the parameters are strongly direction dependent, resulting in a large number of unknown parameters even if appropriately constrained physical or phenomenological descriptions are used. This makes calibration a daunting parameter estimation task, that is reviewed from a signal processing perspective in this article.Comment: 12 pages, 7 figures, 20 subfigures The title quoted in the meta-data is the title after release / final editing

Classification of Radio Galaxies with trainable COSFIRE filters

Radio galaxies exhibit a rich diversity of characteristics and emit radio emissions through a variety of radiation mechanisms, making their classification into distinct types based on morphology a complex challenge. To address this challenge effectively, we introduce an innovative approach for radio galaxy classification using COSFIRE filters. These filters possess the ability to adapt to both the shape and orientation of prototype patterns within images. The COSFIRE approach is explainable, learning-free, rotation-tolerant, efficient, and does not require a huge training set. To assess the efficacy of our method, we conducted experiments on a benchmark radio galaxy data set comprising of 1180 training samples and 404 test samples. Notably, our approach achieved an average accuracy rate of 93.36\%. This achievement outperforms contemporary deep learning models, and it is the best result ever achieved on this data set. Additionally, COSFIRE filters offer better computational performance, $\sim$20$\times$ fewer operations than the DenseNet-based competing method (when comparing at the same accuracy). Our findings underscore the effectiveness of the COSFIRE filter-based approach in addressing the complexities associated with radio galaxy classification. This research contributes to advancing the field by offering a robust solution that transcends the orientation challenges intrinsic to radio galaxy observations. Our method is versatile in that it is applicable to various image classification approaches.Comment: 11 pages, 7 figures, submitted for review at MNRAS journa

Deep supervised hashing for fast retrieval of radio image cubes

The shear number of sources that will be detected by next-generation radio surveys will be astronomical, which will result in serendipitous discoveries. Data-dependent deep hashing algorithms have been shown to be efficient at image retrieval tasks in the fields of computer vision and multimedia. However, there are limited applications of these methodologies in the field of astronomy. In this work, we utilize deep hashing to rapidly search for similar images in a large database. The experiment uses a balanced dataset of 2708 samples consisting of four classes: Compact, FRI, FRII, and Bent. The performance of the method was evaluated using the mean average precision (mAP) metric where a precision of 88.5\% was achieved. The experimental results demonstrate the capability to search and retrieve similar radio images efficiently and at scale. The retrieval is based on the Hamming distance between the binary hash of the query image and those of the reference images in the database.Comment: 4 pages, 4 figure

Advances on the morphological classification of radio galaxiesreview: A review

Modern radio telescopes will generate, on a daily basis, data sets on the scale of exabytes for systems like the Square Kilometre Array (SKA). Massive data sets are a source of unknown and rare astrophysical phenomena that lead to discoveries. Nonetheless, this is only plausible with the exploitation of machine learning to complement human-aided and traditional statistical techniques. Recently, there has been a surge in scientific publications focusing on the use of machine/deep learning in radio astronomy, addressing challenges such as source extraction, morphological classification, and anomaly detection. This study provides a comprehensive and concise overview of the use of machine learning techniques for the morphological classification of radio galaxies. It summarizes the recent literature on this topic, highlighting the main challenges, achievements, state-of-the-art methods, and the future research directions in the field. The application of machine learning in radio astronomy has led to a new paradigm shift and a revolution in the automation of complex data processes. However, the optimal exploitation of machine/deep learning in radio astronomy, calls for continued collaborative efforts in the creation of high-resolution annotated data sets. This is especially true in the case of modern telescopes like MeerKAT and the LOw-Frequency ARray (LOFAR). Additionally, it is important to consider the potential benefits of utilizing multi-channel data cubes and algorithms that can leverage massive datasets without relying solely on annotated datasets for radio galaxy classification.<br/

UAV-aided calibration for commissioning of phased array radio telescopes

Calibration of antenna positions and instrumental response is a crucial step in the commissioning of a phased array radio telescope. The Low Frequency Aperture Array system of the Square Kilometre Array (SKA) is envisaged to consist of about 131,000 antennas. In this paper, we propose a strategy to efficiently conduct commissioning calibration of such a large phased array radio telescope using a near-field probe mounted on an nmanned Aerial Vehicle (UAV). We demonstrate the effectiveness of the proposed method using simulations. This indicates that potentially cost-saving relaxation of requirements on placement accuracy is possible. We also propose to validate this method in practice using the Low Frequency Array (LOFAR)