A fast and exact ww-stacking and ww-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, whilst 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 field of view MWA 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 whilst still maintaining both speed and accuracy.Comment: 9 Figures, 19 Pages. Accepted to Ap

IVOA Recommendation: Data Model for Astronomical DataSet Characterisation

This document defines the high level metadata necessary to describe the physical parameter space of observed or simulated astronomical data sets, such as 2D-images, data cubes, X-ray event lists, IFU data, etc.. The Characterisation data model is an abstraction which can be used to derive a structured description of any relevant data and thus to facilitate its discovery and scientific interpretation. The model aims at facilitating the manipulation of heterogeneous data in any VO framework or portal. A VO Characterisation instance can include descriptions of the data axes, the range of coordinates covered by the data, and details of the data sampling and resolution on each axis. These descriptions should be in terms of physical variables, independent of instrumental signatures as far as possible. Implementations of this model has been described in the IVOA Note available at: http://www.ivoa.net/Documents/latest/ImplementationCharacterisation.html Utypes derived from this version of the UML model are listed and commented in the following IVOA Note: http://www.ivoa.net/Documents/latest/UtypeListCharacterisationDM.html An XML schema has been build up from the UML model and is available at: http://www.ivoa.net/xml/Characterisation/Characterisation-v1.11.xsdComment: http://www.ivoa.ne

View Selection with Geometric Uncertainty Modeling

Estimating positions of world points from features observed in images is a key problem in 3D reconstruction, image mosaicking,simultaneous localization and mapping and structure from motion. We consider a special instance in which there is a dominant ground plane $\mathcal{G}$ viewed from a parallel viewing plane $\mathcal{S}$ above it. Such instances commonly arise, for example, in aerial photography. Consider a world point $g \in \mathcal{G}$ and its worst case reconstruction uncertainty $\varepsilon(g,\mathcal{S})$ obtained by merging \emph{all} possible views of $g$ chosen from $\mathcal{S}$. We first show that one can pick two views $s_p$ and $s_q$ such that the uncertainty $\varepsilon(g,\{s_p,s_q\})$ obtained using only these two views is almost as good as (i.e. within a small constant factor of) $\varepsilon(g,\mathcal{S})$. Next, we extend the result to the entire ground plane $\mathcal{G}$ and show that one can pick a small subset of $\mathcal{S'} \subseteq \mathcal{S}$ (which grows only linearly with the area of $\mathcal{G}$) and still obtain a constant factor approximation, for every point $g \in \mathcal{G}$, to the minimum worst case estimate obtained by merging all views in $\mathcal{S}$. Finally, we present a multi-resolution view selection method which extends our techniques to non-planar scenes. We show that the method can produce rich and accurate dense reconstructions with a small number of views. Our results provide a view selection mechanism with provable performance guarantees which can drastically increase the speed of scene reconstruction algorithms. In addition to theoretical results, we demonstrate their effectiveness in an application where aerial imagery is used for monitoring farms and orchards

Asymmetric Protocols for Scalable High-Rate Measurement-Device-Independent Quantum Key Distribution Networks

Measurement-device-independent quantum key distribution (MDI-QKD) can eliminate detector side channels and prevent all attacks on detectors. The future of MDI-QKD is a quantum network that provides service to many users over untrusted relay nodes. In a real quantum network, the losses of various channels are different and users are added and deleted over time. To adapt to these features, we propose a type of protocols that allow users to independently choose their optimal intensity settings to compensate for different channel losses. Such protocol enables a scalable high-rate MDI-QKD network that can easily be applied for channels of different losses and allows users to be dynamically added/deleted at any time without affecting the performance of existing users.Comment: Changed the title to better represent the generality of our method, and added more discussions on its application to alternative protocols (in Sec. II, the new Table II, and Appendix E with new Fig. 9). Added more conceptual explanations in Sec. II on the difference between X and Z bases in MDI-QKD. Added additional discussions on security of the scheme in Sec. II and Appendix

Bottom-Up and Top-Down Reasoning with Hierarchical Rectified Gaussians

Convolutional neural nets (CNNs) have demonstrated remarkable performance in recent history. Such approaches tend to work in a unidirectional bottom-up feed-forward fashion. However, practical experience and biological evidence tells us that feedback plays a crucial role, particularly for detailed spatial understanding tasks. This work explores bidirectional architectures that also reason with top-down feedback: neural units are influenced by both lower and higher-level units. We do so by treating units as rectified latent variables in a quadratic energy function, which can be seen as a hierarchical Rectified Gaussian model (RGs). We show that RGs can be optimized with a quadratic program (QP), that can in turn be optimized with a recurrent neural network (with rectified linear units). This allows RGs to be trained with GPU-optimized gradient descent. From a theoretical perspective, RGs help establish a connection between CNNs and hierarchical probabilistic models. From a practical perspective, RGs are well suited for detailed spatial tasks that can benefit from top-down reasoning. We illustrate them on the challenging task of keypoint localization under occlusions, where local bottom-up evidence may be misleading. We demonstrate state-of-the-art results on challenging benchmarks.Comment: To appear in CVPR 201

Multiparameter tests of general relativity using multiband gravitational-wave observations

In this Letter we show that multiband observations of stellar-mass binary black holes by the next generation of ground-based observatories (3G) and the space-based Laser Interferometer Space Antenna (LISA) would facilitate a comprehensive test of general relativity by simultaneously measuring all the post-Newtonian (PN) coefficients. Multiband observations would measure most of the known PN phasing coefficients to an accuracy below a few percent---two orders-of-magnitude better than the best bounds achievable from even `golden' binaries in the 3G or LISA bands. Such multiparameter bounds would play a pivotal role in constraining the parameter space of modified theories of gravity beyond general relativity.Comment: 7 pages, 4 figures. v3: version published in PR

Wideband Super-resolution Imaging in Radio Interferometry via Low Rankness and Joint Average Sparsity Models (HyperSARA)

We propose a new approach within the versatile framework of convex optimization to solve the radio-interferometric wideband imaging problem. Our approach, dubbed HyperSARA, solves a sequence of weighted nuclear norm and l21 minimization problems promoting low rankness and joint average sparsity of the wideband model cube. On the one hand, enforcing low rankness enhances the overall resolution of the reconstructed model cube by exploiting the correlation between the different channels. On the other hand, promoting joint average sparsity improves the overall sensitivity by rejecting artefacts present on the different channels. An adaptive Preconditioned Primal-Dual algorithm is adopted to solve the minimization problem. The algorithmic structure is highly scalable to large data sets and allows for imaging in the presence of unknown noise levels and calibration errors. We showcase the superior performance of the proposed approach, reflected in high-resolution images on simulations and real VLA observations with respect to single channel imaging and the CLEAN-based wideband imaging algorithm in the WSCLEAN software. Our MATLAB code is available online on GITHUB

Measurements in two bases are sufficient for certifying high-dimensional entanglement

High-dimensional encoding of quantum information provides a promising method of transcending current limitations in quantum communication. One of the central challenges in the pursuit of such an approach is the certification of high-dimensional entanglement. In particular, it is desirable to do so without resorting to inefficient full state tomography. Here, we show how carefully constructed measurements in two bases (one of which is not orthonormal) can be used to faithfully and efficiently certify bipartite high-dimensional states and their entanglement for any physical platform. To showcase the practicality of this approach under realistic conditions, we put it to the test for photons entangled in their orbital angular momentum. In our experimental setup, we are able to verify 9-dimensional entanglement for a pair of photons on a 11-dimensional subspace each, at present the highest amount certified without any assumptions on the state.Comment: 11+14 pages, 2+7 figure