Novel perspectives gained from new reconstruction algorithms

Since the 1970s, much of traditional interferometric imaging has been built around variations of the CLEAN algorithm, in both terminology, methodology, and algorithm development. Recent developments in applying new algorithms from convex optimization to interferometry has allowed old concepts to be viewed from a new perspective, ranging from image restoration to the development of computationally distributed algorithms. We present how this has ultimately led the authors to new perspectives in wide-field imaging, allowing for the first full individual non-coplanar corrections applied during imaging over extremely wide-fields of view for the Murchison Widefield Array (MWA) telescope. Furthermore, this same mathematical framework has provided a novel understanding of wide-band polarimetry at low frequencies, where instrumental channel depolarization can be corrected through the new δ λ2 -projection algorithm. This is a demonstration that new algorithm development outside of traditional radio astronomy is valuable for the new theoretical and practical perspectives gained. These perspectives are timely with the next generation of radio telescopes coming online

Sparse Bayesian mass-mapping with uncertainties: Full sky observations on the celestial sphere

To date weak gravitational lensing surveys have typically been restricted to small fields of view, such that the flat-sky approximation has been sufficiently satisfied. However, with Stage IV surveys (e.g. LSST and Euclid) imminent, extending mass-mapping techniques to the sphere is a fundamental necessity. As such, we extend the sparse hierarchical Bayesian massmapping formalism presented in previous work to the spherical sky. For the first time, this allows us to construct maximum a posteriori spherical weak lensing dark-matter mass-maps, with principled Bayesian uncertainties, without imposing or assuming Gaussianty. We solve the spherical mass-mapping inverse problem in the analysis setting adopting a sparsity promoting Laplacetype wavelet prior, though this theoretical framework supports all log-concave posteriors. Our spherical mass-mapping formalism facilitates principled statistical interpretation of reconstructions. We apply our framework to convergence reconstruction on high resolution N-body simulations with pseudo-Euclid masking, polluted with a variety of realistic noise levels, and show a significant increase in reconstruction fidelity compared to standard approaches. Furthermore, we perform the largest joint reconstruction to date of the majority of publicly available shear observational data sets (combining DESY1, KiDS450, and CFHTLens) and find that our formalism recovers a convergence map with significantly enhanced small-scale detail. Within our Bayesian framework we validate, in a statistically rigorous manner, the community’s intuition regarding the need to smooth spherical Kaiser-Squires estimates to provide physically meaningful convergence maps. Such approaches cannot reveal the small-scale physical structures that we recover within our framework

ww-stacking ww-projection hybrid algorithm for wide-field interferometric imaging: implementation details and improvements

We present a detailed discussion of the implementation strategies for a recently developed $w$-stacking $w$-projection hybrid algorithm used to reconstruct wide-field interferometric images. In particular, we discuss the methodology used to deploy the algorithm efficiently on a supercomputer via use of a Message Passing Interface (MPI) $k$-means clustering technique to achieve efficient construction and application of non co-planar effects. Additionally, we show that the use of conjugate symmetry increases the algorithms performance by imaging an interferometric observation of Fornax A from the Murchison Widefield Array (MWA). We perform exact non-coplanar wide-field correction for 126.6 million visibilities using 50 nodes of a computing cluster. The $w$-projection kernel construction takes only 15 minutes, demonstrating that the implementation is both fast and efficient.Comment: 10 Pages, 2 Figures. arXiv admin note: text overlap with arXiv:1807.0923

A Fast and Exact w-stacking and w-projection Hybrid Algorithm for Wide-field Interferometric Imaging

The standard wide-field imaging technique, the w-projection, allows correction for wide fields of view for non-coplanar radio interferometric arrays. However, calculating exact corrections for each measurement has not been possible due to the amount of computation required at high resolution and with the large number of visibilities from current interferometers. The required accuracy and computational cost of these corrections is one of the largest unsolved challenges facing next-generation radio interferometers such as the Square Kilometre Array. We show that the same calculation can be performed with a radially symmetric w-projection kernel, where we use one-dimensional adaptive quadrature to calculate the resulting Hankel transform, decreasing the computation required for kernel generation by several orders of magnitude, while preserving the accuracy. We confirm that the radial w-projection kernel is accurate to approximately 1% by imaging the zero-spacing with an added w-term. We demonstrate the potential of our radially symmetric w-projection kernel via sparse image reconstruction, using the software package PURIFY. We develop a distributed w-stacking and w-projection hybrid algorithm. We apply this algorithm to individually correct for non-coplanar effects in 17.5 million visibilities over a 25 by 25 degree FoV Murchison Widefield Array observation for image reconstruction. Such a level of accuracy and scalability is not possible with standard w-projection kernel generation methods. This demonstrates that we can scale to a large number of measurements with large image sizes while still maintaining both speed and accuracy

Switching to Once-Daily Liraglutide From Twice-Daily Exenatide Further Improves Glycemic Control in Patients With Type 2 Diabetes Using Oral Agents

OBJECTIVETo evaluate efficacy and safety of switching from twice-daily exenatide to once-daily liraglutide or of 40 weeks of continuous liraglutide therapy.RESEARCH DESIGN AND METHODSWhen added to oral antidiabetes drugs in a 26-week randomized trial (Liraglutide Effect and Action in Diabetes [LEAD]-6), liraglutide more effectively improved A1C, fasting plasma glucose, and the homeostasis model of β-cell function (HOMA-B) than exenatide, with less persistent nausea and hypoglycemia. In this 14-week extension of LEAD-6, patients switched from 10 μg twice-daily exenatide to 1.8 mg once-daily liraglutide or continued liraglutide.RESULTSSwitching from exenatide to liraglutide further and significantly reduced A1C (0.32%), fasting plasma glucose (0.9 mmol/l), body weight (0.9 kg), and systolic blood pressure (3.8 mmHg) with minimal minor hypoglycemia (1.30 episodes/patient-year) or nausea (3.2%). Among patients continuing liraglutide, further significant decreases in body weight (0.4 kg) and systolic blood pressure (2.2 mmHg) occurred with 0.74 episodes/patient-year of minor hypoglycemia and 1.5% experiencing nausea.CONCLUSIONSConversion from exenatide to liraglutide is well tolerated and provides additional glycemic control and cardiometabolic benefits