Direct Fourier Transformation Research Articles

A novel approach to visibility-space modelling of interferometric gravitational lens observations at high angular resolution

ABSTRACT We present a new gravitational lens modelling technique designed to model high-resolution interferometric observations with large numbers of visibilities without the need to pre-average the data in time or frequency. We demonstrate the accuracy of the method using validation tests on mock observations. Using small data sets with ∼103 visibilities, we first compare our approach with the more traditional direct Fourier transform (DFT) implementation and direct linear solver. Our tests indicate that our source inversion is indistinguishable from that of the DFT. Our method also infers lens parameters to within 1 to 2 per cent of both the ground truth and DFT, given sufficiently high signal-to-noise ratio (SNR). When the SNR is as low as 5, both approaches lead to errors of several tens of per cent in the lens parameters and a severely disrupted source structure, indicating that this is related to the SNR and choice of priors rather than the modelling technique itself. We then analyse a large data set with ∼108 visibilities and a SNR matching real global Very Long Baseline Interferometry observations of the gravitational lens system MG J0751+2716. The size of the data is such that it cannot be modelled with traditional implementations. Using our novel technique, we find that we can infer the lens parameters and the source brightness distribution, respectively, with an RMS error of 0.25 and 0.97 per cent relative to the ground truth.

Direct wide-field radio imaging in real-time at high time resolution using antenna electric fields

ABSTRACTThe recent demonstration of a real-time direct imaging radio interferometry correlator represents a new capability in radio astronomy. However, wide-field imaging with this method is challenging since wide-field effects and array non-coplanarity degrade image quality if not compensated for. Here, we present an alternative direct imaging correlation strategy using a direct Fourier transform (DFT), modelled as a linear operator facilitating a matrix multiplication between the DFT matrix and a vector of the electric fields from each antenna. This offers perfect correction for wide field and non-coplanarity effects. When implemented with data from the Long Wavelength Array (LWA), it offers comparable computational performance to previously demonstrated direct imaging techniques, despite having a theoretically higher floating point cost. It also has additional benefits, such as imaging sparse arrays and control over which sky coordinates are imaged, allowing variable pixel placement across an image. It is in practice a highly flexible and efficient method of direct radio imaging when implemented on suitable arrays. A functioning electric field direct imaging architecture using the DFT is presented, alongside an exploration of techniques for wide-field imaging similar to those in visibility-based imaging, and an explanation of why they do not fit well to imaging directly with the digitized electric field data. The DFT imaging method is demonstrated on real data from the LWA telescope, alongside a detailed performance analysis, as well as an exploration of its applicability to other arrays.

Numerical Prediction of Aerodynamic Noise Generated from an Aircraft in Low Mach Number Flight

AbstractThe paper describes numerical prediction of aerodynamic noise generated from an Aircraft. Simulation of turbulent flow is done solving the incompressible Navier‐Stokes equation, where turbulence is modeled applying the orthogonal subgrid scale (OSGS) method with dynamical subscales. Because of comparison, the same simulation is done using the LES (Large Eddy simulation). It is shown how simulation of turbulent flow affects the prediction of acoustic sources calculated using Lighthill's analogy. Translation from the time to frequency domain is done through DFT (Direct Fourier Transform), which gives smaller usage of memory. Acoustic sources are used in the inhomogeneous Helmholtz equation to simulate pressure wave propagation in the domain. It is shown that OSGS with dynamical subscales gives better representation of the spectrum. Overall, better prediction of energy transfer across large and small eddies will give better allocation and presentation of acoustics sources. These sources will change wave propagation of the pressure in the acoustic field. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Fast direct fourier reconstruction of radial and PROPELLER MRI data using the chirp transform algorithm on graphics hardware

To develop and test a new algorithm for fast direct Fourier transform (DrFT) reconstruction of MR data on non-Cartesian trajectories composed of lines with equally spaced points. The DrFT, which is normally used as a reference in evaluating the accuracy of other reconstruction methods, can reconstruct images directly from non-Cartesian MR data without interpolation. However, DrFT reconstruction involves substantially intensive computation, which makes the DrFT impractical for clinical routine applications. In this article, the Chirp transform algorithm was introduced to accelerate the DrFT reconstruction of radial and Periodically Rotated Overlapping ParallEL Lines with Enhanced Reconstruction (PROPELLER) MRI data located on the trajectories that are composed of lines with equally spaced points. The performance of the proposed Chirp transform algorithm-DrFT algorithm was evaluated by using simulation and in vivo MRI data. After implementing the algorithm on a graphics processing unit, the proposed Chirp transform algorithm-DrFT algorithm achieved an acceleration of approximately one order of magnitude, and the speed-up factor was further increased to approximately three orders of magnitude compared with the traditional single-thread DrFT reconstruction. Implementation the Chirp transform algorithm-DrFT algorithm on the graphics processing unit can efficiently calculate the DrFT reconstruction of the radial and PROPELLER MRI data.

RST Invariant Digital Watermarking Based on Image Representation by Wedges and Rings

This paper describes a new image watermarking scheme invariant to rotation, scaling and translation (RST) attacks. For obtaining the invariance properties we propose to present an image of watermark by wedges and rings to convert its rotation to shift and then utilize the shift invariance property of the Direct Fourier Transform (DFT). But in contrast to conversional schemes based on the Fourier-Mellin transform (FMT), we do not use a log-polar mapping (LPM). As a result, our scheme preserves high quality of original image since it is not underwent to LPM For withstanding against JPEG compression, noise addition and low-pass (LP) filtering attacks a low frequency watermark is embedded into middle frequencies of the original image. Experiments with various attacks show the robustness of the proposed scheme.

Direct reconstruction of MR images from data acquired on a non-Cartesian grid using an equal-phase-line algorithm.

The equal-phase line (EPL) algorithm is proposed as a means of allowing rapid Fourier transform (FT) reconstruction of MR image data acquired on a non-Cartesian grid. The pixels on the image are grouped according to their positions. The pixels in a group have the same phase in the complex exponential function -exp[j2pi(xu + yv)] and receive the same contribution from a data point. Each group is related to an EPL in the image space. The contribution of a data point can then be distributed to the pixels along the EPLs. The described EPL algorithm enables a decrease of the reconstruction time to about 40% of the direct FT (DrFT) for the non-Cartesian data. A numerical phantom and two sets of in vivo spiral data were used to investigate an optimal number of the EPLs and to measure the reconstruction time. The EPL algorithm runs nearly as fast as the look-up table (LUT) method (Dale et al. IEEE Trans Med Imaging 2001;20:207-217), but it does not require a large memory to store the coefficients in advance, as is required in the LUT method. Thus, the EPL algorithm can be used to reconstruct images up to 512 x 512 pixels in size in a PC of limited memory, and may be more conveniently applied to a multiprocessor system.